On the singular perturbations for fractional differential equation.

Science.gov (United States)

Atangana, Abdon

2014-01-01

The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method.

Ultrasound speckle reduction based on fractional order differentiation.

Science.gov (United States)

Shao, Dangguo; Zhou, Ting; Liu, Fan; Yi, Sanli; Xiang, Yan; Ma, Lei; Xiong, Xin; He, Jianfeng

2017-07-01

Ultrasound images show a granular pattern of noise known as speckle that diminishes their quality and results in difficulties in diagnosis. To preserve edges and features, this paper proposes a fractional differentiation-based image operator to reduce speckle in ultrasound. An image de-noising model based on fractional partial differential equations with balance relation between k (gradient modulus threshold that controls the conduction) and v (the order of fractional differentiation) was constructed by the effective combination of fractional calculus theory and a partial differential equation, and the numerical algorithm of it was achieved using a fractional differential mask operator. The proposed algorithm has better speckle reduction and structure preservation than the three existing methods [P-M model, the speckle reducing anisotropic diffusion (SRAD) technique, and the detail preserving anisotropic diffusion (DPAD) technique]. And it is significantly faster than bilateral filtering (BF) in producing virtually the same experimental results. Ultrasound phantom testing and in vivo imaging show that the proposed method can improve the quality of an ultrasound image in terms of tissue SNR, CNR, and FOM values.

Fractional and sequential recovery of inorganic contaminants from acid mine drainage using cryptocrystalline magnesite

CSIR Research Space (South Africa)

Masindi, Vhahangwele

2017-06-01

Full Text Available This study evaluated the fractional and sequential recovery of inorganic contaminants from acid mine drainage (AMD) using cryptocrystalline magnesite. Batch experimental approach was used to fulfil the goals of this study. The obtained results...

Reduced differential transform method for partial differential equations within local fractional derivative operators

Directory of Open Access Journals (Sweden)

Hossein Jafari

2016-04-01

Full Text Available The non-differentiable solution of the linear and non-linear partial differential equations on Cantor sets is implemented in this article. The reduced differential transform method is considered in the local fractional operator sense. The four illustrative examples are given to show the efficiency and accuracy features of the presented technique to solve local fractional partial differential equations.

On the Singular Perturbations for Fractional Differential Equation

Directory of Open Access Journals (Sweden)

Abdon Atangana

2014-01-01

Full Text Available The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method.

On-line dynamic fractionation and automatic determination of inorganic phosphorous in environmental solid substrates exploiting sequential injection microcolumn extraction and flow injection analysi

DEFF Research Database (Denmark)

Buanuam, Janya; Miró, Manuel; Hansen, Elo Harald

2006-01-01

Sequential injection microcolumn extraction (SI-MCE) based on the implementation of a soil containing microcartridge as external reactor in a sequential injection network is, for the first time, proposed for dynamic fractionation of macronutrients in environmental solids, as exemplified by the pa......Sequential injection microcolumn extraction (SI-MCE) based on the implementation of a soil containing microcartridge as external reactor in a sequential injection network is, for the first time, proposed for dynamic fractionation of macronutrients in environmental solids, as exemplified...... by the partitioning of inorganic phosphorous in agricultural soils. The on-line fractionation method capitalises on the accurate metering and sequential exposure of the various extractants to the solid sample by application of programmable flow as precisely coordinated by a syringe pump. Three different soil phase...... associations for phosphorus, that is, exchangeable, Al- and Fe-bound and Ca-bound fractions, were elucidated by accommodation in the flow manifold of the 3 steps of the Hietjles-Litjkema (HL) scheme involving the use of 1.0 M NH4Cl, 0.1 M NaOH and 0.5 M HCl, respectively, as sequential leaching reagents...

Fractional Differential and Integral Inequalities with Applications

Science.gov (United States)

2016-02-14

Dynamic Systems and Applications (07 2013) Aghalaya S. Vatsala, Bhuvaneswari Sambandham. Laplace Transform Method for Sequential CaputoFractional...coupled minimal and maximal solutions for such an equation and a numerical example is provided as an application of the theoretical results. The... Applications The views, opinions and/or findings contained in this report are those of the author(s) and should not contrued as an official Department of

Analytical Solutions for Multi-Time Scale Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion and Their Applications

Directory of Open Access Journals (Sweden)

Xiao-Li Ding

2018-01-01

Full Text Available In this paper, we investigate analytical solutions of multi-time scale fractional stochastic differential equations driven by fractional Brownian motions. We firstly decompose homogeneous multi-time scale fractional stochastic differential equations driven by fractional Brownian motions into independent differential subequations, and give their analytical solutions. Then, we use the variation of constant parameters to obtain the solutions of nonhomogeneous multi-time scale fractional stochastic differential equations driven by fractional Brownian motions. Finally, we give three examples to demonstrate the applicability of our obtained results.

Characterization of plant-derived carbon and phosphorus in lakes by sequential fractionation and NMR spectroscopy

Energy Technology Data Exchange (ETDEWEB)

Liu, Shasha [College of Water Sciences, Beijing Normal University, Beijing 100875 (China); State Key Laboratory of Environment Criteria and Risk Assessment, Chinese Research Academy of Environmental Sciences, Beijing 100012 (China); Zhu, Yuanrong, E-mail: zhuyuanrong07@mails.ucas.ac.cn [State Key Laboratory of Environment Criteria and Risk Assessment, Chinese Research Academy of Environmental Sciences, Beijing 100012 (China); Wu, Fengchang, E-mail: wufengchang@vip.skleg.cn [State Key Laboratory of Environment Criteria and Risk Assessment, Chinese Research Academy of Environmental Sciences, Beijing 100012 (China); Meng, Wei [State Key Laboratory of Environment Criteria and Risk Assessment, Chinese Research Academy of Environmental Sciences, Beijing 100012 (China); He, Zhongqi [USDA-ARS Southern Regional Research Center, 1100 Robert E Lee Blvd, New Orleans, LA 70124 (United States); Giesy, John P. [State Key Laboratory of Environment Criteria and Risk Assessment, Chinese Research Academy of Environmental Sciences, Beijing 100012 (China); Department of Biomedical and Veterinary Biosciences and Toxicology Centre, University of Saskatchewan, Saskatoon, Saskatchewan (Canada)

2016-10-01

Although debris from aquatic macrophytes is one of the most important endogenous sources of organic matter (OM) and nutrients in lakes, its biogeochemical cycling and contribution to internal load of nutrients in eutrophic lakes are still poorly understood. In this study, sequential fractionation by H{sub 2}O, 0.1 M NaOH and 1.0 M HCl, combined with {sup 13}C and {sup 31}P NMR spectroscopy, was developed and used to characterize organic carbon (C) and phosphorus (P) in six aquatic plants collected from Tai Lake (Ch: Taihu), China. Organic matter, determined by total organic carbon (TOC), was unequally distributed in H{sub 2}O (21.2%), NaOH (29.9%), HCl (3.5%) and residual (45.3%) fractions. For P in debris of aquatic plants, 53.3% was extracted by H{sub 2}O, 31.9% by NaOH, and 11% by HCl, with 3.8% in residual fractions. Predominant OM components extracted by H{sub 2}O and NaOH were carbohydrates, proteins and aliphatic acids. Inorganic P (P{sub i}) was the primary form of P in H{sub 2}O fractions, whereas organic P (P{sub o}) was the primary form of P in NaOH fractions. The subsequent HCl fractions extracted fewer species of C and P. Some non-extractable carbohydrates, aromatics and metal phytate compounds remained in residual fractions. Based on sequential extraction and NMR analysis, it was proposed that those forms of C (54.7% of TOC) and P (96.2% of TP) in H{sub 2}O, NaOH and HCl fractions are potentially released to overlying water as labile components, while those in residues are stable and likely preserved in sediments of lakes. These results will be helpful in understanding internal loading of nutrients from debris of aquatic macrophytes and their recycling in lakes. - Highlights: • Sequential fractionation combined with NMR analysis was applied on aquatic plants. • Labile and stable C and P forms in aquatic plants were characterized. • 54.7% of OM and 96.2% of P in aquatic plants are potentially available. • 45.3% of OM and 3.8% of P in aquatic

Solution of fractional differential equations by using differential transform method

International Nuclear Information System (INIS)

Arikoglu, Aytac; Ozkol, Ibrahim

2007-01-01

In this study, we implement a well known transformation technique, Differential Transform Method (DTM), to the area of fractional differential equations. Theorems that never existed before are introduced with their proofs. Also numerical examples are carried out for various types of problems, including the Bagley-Torvik, Ricatti and composite fractional oscillation equations for the application of the method. The results obtained are in good agreement with the existing ones in open literature and it is shown that the technique introduced here is robust, accurate and easy to apply

Solution of fractional differential equations by using differential transform method

Energy Technology Data Exchange (ETDEWEB)

Arikoglu, Aytac [Istanbul Technical University, Faculty of Aeronautics and Astronautics, Department of Aeronautical Engineering, Maslak, TR-34469 Istanbul (Turkey); Ozkol, Ibrahim [Istanbul Technical University, Faculty of Aeronautics and Astronautics, Department of Aeronautical Engineering, Maslak, TR-34469 Istanbul (Turkey)]. E-mail: ozkol@itu.edu.tr

2007-12-15

In this study, we implement a well known transformation technique, Differential Transform Method (DTM), to the area of fractional differential equations. Theorems that never existed before are introduced with their proofs. Also numerical examples are carried out for various types of problems, including the Bagley-Torvik, Ricatti and composite fractional oscillation equations for the application of the method. The results obtained are in good agreement with the existing ones in open literature and it is shown that the technique introduced here is robust, accurate and easy to apply.

Hadamard-type fractional differential equations, inclusions and inequalities

CERN Document Server

Ahmad, Bashir; Ntouyas, Sotiris K; Tariboon, Jessada

2017-01-01

This book focuses on the recent development of fractional differential equations, integro-differential equations, and inclusions and inequalities involving the Hadamard derivative and integral. Through a comprehensive study based in part on their recent research, the authors address the issues related to initial and boundary value problems involving Hadamard type differential equations and inclusions as well as their functional counterparts. The book covers fundamental concepts of multivalued analysis and introduces a new class of mixed initial value problems involving the Hadamard derivative and Riemann-Liouville fractional integrals. In later chapters, the authors discuss nonlinear Langevin equations as well as coupled systems of Langevin equations with fractional integral conditions. Focused and thorough, this book is a useful resource for readers and researchers interested in the area of fractional calculus.

Robust fractional order differentiators using generalized modulating functions method

KAUST Repository

Liu, Dayan

2015-02-01

This paper aims at designing a fractional order differentiator for a class of signals satisfying a linear differential equation with unknown parameters. A generalized modulating functions method is proposed first to estimate the unknown parameters, then to derive accurate integral formulae for the left-sided Riemann-Liouville fractional derivatives of the studied signal. Unlike the improper integral in the definition of the left-sided Riemann-Liouville fractional derivative, the integrals in the proposed formulae can be proper and be considered as a low-pass filter by choosing appropriate modulating functions. Hence, digital fractional order differentiators applicable for on-line applications are deduced using a numerical integration method in discrete noisy case. Moreover, some error analysis are given for noise error contributions due to a class of stochastic processes. Finally, numerical examples are given to show the accuracy and robustness of the proposed fractional order differentiators.

Robust fractional order differentiators using generalized modulating functions method

KAUST Repository

Liu, Dayan; Laleg-Kirati, Taous-Meriem

2015-01-01

This paper aims at designing a fractional order differentiator for a class of signals satisfying a linear differential equation with unknown parameters. A generalized modulating functions method is proposed first to estimate the unknown parameters, then to derive accurate integral formulae for the left-sided Riemann-Liouville fractional derivatives of the studied signal. Unlike the improper integral in the definition of the left-sided Riemann-Liouville fractional derivative, the integrals in the proposed formulae can be proper and be considered as a low-pass filter by choosing appropriate modulating functions. Hence, digital fractional order differentiators applicable for on-line applications are deduced using a numerical integration method in discrete noisy case. Moreover, some error analysis are given for noise error contributions due to a class of stochastic processes. Finally, numerical examples are given to show the accuracy and robustness of the proposed fractional order differentiators.

Analytical Solutions for Multi-Time Scale Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion and Their Applications

OpenAIRE

Xiao-Li Ding; Juan J. Nieto

2018-01-01

In this paper, we investigate analytical solutions of multi-time scale fractional stochastic differential equations driven by fractional Brownian motions. We firstly decompose homogeneous multi-time scale fractional stochastic differential equations driven by fractional Brownian motions into independent differential subequations, and give their analytical solutions. Then, we use the variation of constant parameters to obtain the solutions of nonhomogeneous multi-time scale fractional stochast...

On Fractional Order Hybrid Differential Equations

Directory of Open Access Journals (Sweden)

Mohamed A. E. Herzallah

2014-01-01

Full Text Available We develop the theory of fractional hybrid differential equations with linear and nonlinear perturbations involving the Caputo fractional derivative of order 0<α<1. Using some fixed point theorems we prove the existence of mild solutions for two types of hybrid equations. Examples are given to illustrate the obtained results.

A procedure to construct exact solutions of nonlinear fractional differential equations.

Science.gov (United States)

Güner, Özkan; Cevikel, Adem C

2014-01-01

We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations. The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. We apply the Exp-function method to the time fractional Sharma-Tasso-Olver equation, the space fractional Burgers equation, and the time fractional fmKdV equation. As a result, we obtain some new exact solutions.

An algebraic fractional order differentiator for a class of signals satisfying a linear differential equation

KAUST Repository

Liu, Da-Yan; Tian, Yang; Boutat, Driss; Laleg-Kirati, Taous-Meriem

2015-01-01

This paper aims at designing a digital fractional order differentiator for a class of signals satisfying a linear differential equation to estimate fractional derivatives with an arbitrary order in noisy case, where the input can be unknown or known with noises. Firstly, an integer order differentiator for the input is constructed using a truncated Jacobi orthogonal series expansion. Then, a new algebraic formula for the Riemann-Liouville derivative is derived, which is enlightened by the algebraic parametric method. Secondly, a digital fractional order differentiator is proposed using a numerical integration method in discrete noisy case. Then, the noise error contribution is analyzed, where an error bound useful for the selection of the design parameter is provided. Finally, numerical examples illustrate the accuracy and the robustness of the proposed fractional order differentiator.

An algebraic fractional order differentiator for a class of signals satisfying a linear differential equation

KAUST Repository

Liu, Da-Yan

2015-04-30

This paper aims at designing a digital fractional order differentiator for a class of signals satisfying a linear differential equation to estimate fractional derivatives with an arbitrary order in noisy case, where the input can be unknown or known with noises. Firstly, an integer order differentiator for the input is constructed using a truncated Jacobi orthogonal series expansion. Then, a new algebraic formula for the Riemann-Liouville derivative is derived, which is enlightened by the algebraic parametric method. Secondly, a digital fractional order differentiator is proposed using a numerical integration method in discrete noisy case. Then, the noise error contribution is analyzed, where an error bound useful for the selection of the design parameter is provided. Finally, numerical examples illustrate the accuracy and the robustness of the proposed fractional order differentiator.

Periodicity and positivity of a class of fractional differential equations.

Science.gov (United States)

Ibrahim, Rabha W; Ahmad, M Z; Mohammed, M Jasim

2016-01-01

Fractional differential equations have been discussed in this study. We utilize the Riemann-Liouville fractional calculus to implement it within the generalization of the well known class of differential equations. The Rayleigh differential equation has been generalized of fractional second order. The existence of periodic and positive outcome is established in a new method. The solution is described in a fractional periodic Sobolev space. Positivity of outcomes is considered under certain requirements. We develop and extend some recent works. An example is constructed.

Introduction to fractional and pseudo-differential equations with singular symbols

CERN Document Server

Umarov, Sabir

2015-01-01

The book systematically presents the theories of pseudo-differential operators with symbols singular in dual variables, fractional order derivatives, distributed and variable order fractional derivatives, random walk approximants, and applications of these theories to various initial and multi-point boundary value problems for pseudo-differential equations. Fractional Fokker-Planck-Kolmogorov equations associated with a large class of stochastic processes are presented. A complex version of the theory of pseudo-differential operators with meromorphic symbols based on the recently introduced complex Fourier transform is developed and applied for initial and boundary value problems for systems of complex differential and pseudo-differential equations.

Selective condensation drives partitioning and sequential secretion of cyst wall proteins in differentiating Giardia lamblia.

Directory of Open Access Journals (Sweden)

Christian Konrad

2010-04-01

Full Text Available Controlled secretion of a protective extracellular matrix is required for transmission of the infective stage of a large number of protozoan and metazoan parasites. Differentiating trophozoites of the highly minimized protozoan parasite Giardia lamblia secrete the proteinaceous portion of the cyst wall material (CWM consisting of three paralogous cyst wall proteins (CWP1-3 via organelles termed encystation-specific vesicles (ESVs. Phylogenetic and molecular data indicate that Diplomonads have lost a classical Golgi during reductive evolution. However, neogenesis of ESVs in encysting Giardia trophozoites transiently provides basic Golgi functions by accumulating presorted CWM exported from the ER for maturation. Based on this "minimal Golgi" hypothesis we predicted maturation of ESVs to a trans Golgi-like stage, which would manifest as a sorting event before regulated secretion of the CWM. Here we show that proteolytic processing of pro-CWP2 in maturing ESVs coincides with partitioning of CWM into two fractions, which are sorted and secreted sequentially with different kinetics. This novel sorting function leads to rapid assembly of a structurally defined outer cyst wall, followed by slow secretion of the remaining components. Using live cell microscopy we find direct evidence for condensed core formation in maturing ESVs. Core formation suggests that a mechanism controlled by phase transitions of the CWM from fluid to condensed and back likely drives CWM partitioning and makes sorting and sequential secretion possible. Blocking of CWP2 processing by a protease inhibitor leads to mis-sorting of a CWP2 reporter. Nevertheless, partitioning and sequential secretion of two portions of the CWM are unaffected in these cells. Although these cysts have a normal appearance they are not water resistant and therefore not infective. Our findings suggest that sequential assembly is a basic architectural principle of protective wall formation and requires

Parameters and Fractional Differentiation Orders Estimation for Linear Continuous-Time Non-Commensurate Fractional Order Systems

KAUST Repository

Belkhatir, Zehor; Laleg-Kirati, Taous-Meriem

2017-01-01

This paper proposes a two-stage estimation algorithm to solve the problem of joint estimation of the parameters and the fractional differentiation orders of a linear continuous-time fractional system with non-commensurate orders. The proposed algorithm combines the modulating functions and the first-order Newton methods. Sufficient conditions ensuring the convergence of the method are provided. An error analysis in the discrete case is performed. Moreover, the method is extended to the joint estimation of smooth unknown input and fractional differentiation orders. The performance of the proposed approach is illustrated with different numerical examples. Furthermore, a potential application of the algorithm is proposed which consists in the estimation of the differentiation orders of a fractional neurovascular model along with the neural activity considered as input for this model.

Parameters and Fractional Differentiation Orders Estimation for Linear Continuous-Time Non-Commensurate Fractional Order Systems

KAUST Repository

Belkhatir, Zehor

2017-05-31

This paper proposes a two-stage estimation algorithm to solve the problem of joint estimation of the parameters and the fractional differentiation orders of a linear continuous-time fractional system with non-commensurate orders. The proposed algorithm combines the modulating functions and the first-order Newton methods. Sufficient conditions ensuring the convergence of the method are provided. An error analysis in the discrete case is performed. Moreover, the method is extended to the joint estimation of smooth unknown input and fractional differentiation orders. The performance of the proposed approach is illustrated with different numerical examples. Furthermore, a potential application of the algorithm is proposed which consists in the estimation of the differentiation orders of a fractional neurovascular model along with the neural activity considered as input for this model.

Joint estimation of the fractional differentiation orders and the unknown input for linear fractional non-commensurate system

KAUST Repository

Belkhatir, Zehor

2015-11-05

This paper deals with the joint estimation of the unknown input and the fractional differentiation orders of a linear fractional order system. A two-stage algorithm combining the modulating functions with a first-order Newton method is applied to solve this estimation problem. First, the modulating functions approach is used to estimate the unknown input for a given fractional differentiation orders. Then, the method is combined with a first-order Newton technique to identify the fractional orders jointly with the input. To show the efficiency of the proposed method, numerical examples illustrating the estimation of the neural activity, considered as input of a fractional model of the neurovascular coupling, along with the fractional differentiation orders are presented in both noise-free and noisy cases.

Existence of a coupled system of fractional differential equations

International Nuclear Information System (INIS)

Ibrahim, Rabha W.; Siri, Zailan

2015-01-01

We manage the existence and uniqueness of a fractional coupled system containing Schrödinger equations. Such a system appears in quantum mechanics. We confirm that the fractional system under consideration admits a global solution in appropriate functional spaces. The solution is shown to be unique. The method is based on analytic technique of the fixed point theory. The fractional differential operator is considered from the virtue of the Riemann-Liouville differential operator

Existence of a coupled system of fractional differential equations

Energy Technology Data Exchange (ETDEWEB)

Ibrahim, Rabha W. [Multimedia unit, Department of Computer System and Technology Faculty of Computer Science & IT, University of Malaya, 50603 Kuala Lumpur (Malaysia); Siri, Zailan [Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur (Malaysia)

2015-10-22

We manage the existence and uniqueness of a fractional coupled system containing Schrödinger equations. Such a system appears in quantum mechanics. We confirm that the fractional system under consideration admits a global solution in appropriate functional spaces. The solution is shown to be unique. The method is based on analytic technique of the fixed point theory. The fractional differential operator is considered from the virtue of the Riemann-Liouville differential operator.

Exact solutions to the time-fractional differential equations via local fractional derivatives

Science.gov (United States)

Guner, Ozkan; Bekir, Ahmet

2018-01-01

This article utilizes the local fractional derivative and the exp-function method to construct the exact solutions of nonlinear time-fractional differential equations (FDEs). For illustrating the validity of the method, it is applied to the time-fractional Camassa-Holm equation and the time-fractional-generalized fifth-order KdV equation. Moreover, the exact solutions are obtained for the equations which are formed by different parameter values related to the time-fractional-generalized fifth-order KdV equation. This method is an reliable and efficient mathematical tool for solving FDEs and it can be applied to other non-linear FDEs.

Mercury and trace element fractionation in Almaden soils by application of different sequential extraction procedures

Energy Technology Data Exchange (ETDEWEB)

Sanchez, D.M.; Quejido, A.J.; Fernandez, M.; Hernandez, C.; Schmid, T.; Millan, R.; Gonzalez, M.; Aldea, M.; Martin, R.; Morante, R. [CIEMAT, Madrid (Spain)

2005-04-01

A comparative evaluation of the mercury distribution in a soil sample from Almaden (Spain) has been performed by applying three different sequential extraction procedures, namely, modified BCR (three steps in sequence), Di Giulio-Ryan (four steps in sequence), and a specific SEP developed at CIEMAT (six steps in sequence). There were important differences in the mercury extraction results obtained by the three procedures according to the reagents applied and the sequence of their application. These findings highlight the difficulty of setting a universal SEP to obtain information on metal fractions of different mobility for any soil sample, as well as the requirement for knowledge about the mineralogical and chemical characteristics of the samples. The specific six-step CIEMAT sequential extraction procedure was applied to a soil profile (Ap, Ah, Bt1, and Bt2 horizons). The distribution of mercury and major, minor, and trace elements in the different fractions were determined. The results indicate that mercury is mainly released with 6 M HCl. The strong association of mercury with crystalline iron oxyhydroxides, present in all the horizons of the profile, and/or the solubility of some mercury compounds in such acid can explain this fact. Minor mercury is found in the fraction assigned to oxidizable matter and in the final insoluble residue (cinnabar). (orig.)

Oscillation of a class of fractional differential equations with damping term.

Science.gov (United States)

Qin, Huizeng; Zheng, Bin

2013-01-01

We investigate the oscillation of a class of fractional differential equations with damping term. Based on a certain variable transformation, the fractional differential equations are converted into another differential equations of integer order with respect to the new variable. Then, using Riccati transformation, inequality, and integration average technique, some new oscillatory criteria for the equations are established. As for applications, oscillation for two certain fractional differential equations with damping term is investigated by the use of the presented results.

A remark on fractional differential equation involving I-function

Science.gov (United States)

Mishra, Jyoti

2018-02-01

The present paper deals with the solution of the fractional differential equation using the Laplace transform operator and its corresponding properties in the fractional calculus; we derive an exact solution of a complex fractional differential equation involving a special function known as I-function. The analysis of the some fractional integral with two parameters is presented using the suggested Theorem 1. In addition, some very useful corollaries are established and their proofs presented in detail. Some obtained exact solutions are depicted to see the effect of each fractional order. Owing to the wider applicability of the I-function, we can conclude that, the obtained results in our work generalize numerous well-known results obtained by specializing the parameters.

The improved fractional sub-equation method and its applications to the space–time fractional differential equations in fluid mechanics

International Nuclear Information System (INIS)

Guo, Shimin; Mei, Liquan; Li, Ying; Sun, Youfa

2012-01-01

By introducing a new general ansätz, the improved fractional sub-equation method is proposed to construct analytical solutions of nonlinear evolution equations involving Jumarie's modified Riemann–Liouville derivative. By means of this method, the space–time fractional Whitham–Broer–Kaup and generalized Hirota–Satsuma coupled KdV equations are successfully solved. The obtained results show that the proposed method is quite effective, promising and convenient for solving nonlinear fractional differential equations. -- Highlights: ► We propose a novel method for nonlinear fractional differential equations. ► Two important fractional differential equations in fluid mechanics are solved successfully. ► Some new exact solutions of the fractional differential equations are obtained. ► These solutions will advance the understanding of nonlinear physical phenomena.

Non-asymptotic fractional order differentiators via an algebraic parametric method

KAUST Repository

Liu, Dayan; Gibaru, O.; Perruquetti, Wilfrid

2012-01-01

Recently, Mboup, Join and Fliess [27], [28] introduced non-asymptotic integer order differentiators by using an algebraic parametric estimation method [7], [8]. In this paper, in order to obtain non-asymptotic fractional order differentiators we apply this algebraic parametric method to truncated expansions of fractional Taylor series based on the Jumarie's modified Riemann-Liouville derivative [14]. Exact and simple formulae for these differentiators are given where a sliding integration window of a noisy signal involving Jacobi polynomials is used without complex mathematical deduction. The efficiency and the stability with respect to corrupting noises of the proposed fractional order differentiators are shown in numerical simulations. © 2012 IEEE.

Non-asymptotic fractional order differentiators via an algebraic parametric method

KAUST Repository

Liu, Dayan

2012-08-01

Recently, Mboup, Join and Fliess [27], [28] introduced non-asymptotic integer order differentiators by using an algebraic parametric estimation method [7], [8]. In this paper, in order to obtain non-asymptotic fractional order differentiators we apply this algebraic parametric method to truncated expansions of fractional Taylor series based on the Jumarie\\'s modified Riemann-Liouville derivative [14]. Exact and simple formulae for these differentiators are given where a sliding integration window of a noisy signal involving Jacobi polynomials is used without complex mathematical deduction. The efficiency and the stability with respect to corrupting noises of the proposed fractional order differentiators are shown in numerical simulations. © 2012 IEEE.

A sequential EMT-MET mechanism drives the differentiation of human embryonic stem cells towards hepatocytes.

Science.gov (United States)

Li, Qiuhong; Hutchins, Andrew P; Chen, Yong; Li, Shengbiao; Shan, Yongli; Liao, Baojian; Zheng, Dejin; Shi, Xi; Li, Yinxiong; Chan, Wai-Yee; Pan, Guangjin; Wei, Shicheng; Shu, Xiaodong; Pei, Duanqing

2017-05-03

Reprogramming has been shown to involve EMT-MET; however, its role in cell differentiation is unclear. We report here that in vitro differentiation of hESCs to hepatic lineage undergoes a sequential EMT-MET with an obligatory intermediate mesenchymal phase. Gene expression analysis reveals that Activin A-induced formation of definitive endoderm (DE) accompanies a synchronous EMT mediated by autocrine TGFβ signalling followed by a MET process. Pharmacological inhibition of TGFβ signalling blocks the EMT as well as DE formation. We then identify SNAI1 as the key EMT transcriptional factor required for the specification of DE. Genetic ablation of SNAI1 in hESCs does not affect the maintenance of pluripotency or neural differentiation, but completely disrupts the formation of DE. These results reveal a critical mesenchymal phase during the acquisition of DE, highlighting a role for sequential EMT-METs in both differentiation and reprogramming.

Exact solutions of nonlinear fractional differential equations by (G′/G)-expansion method

International Nuclear Information System (INIS)

Bekir Ahmet; Güner Özkan

2013-01-01

In this paper, we use the fractional complex transform and the (G′/G)-expansion method to study the nonlinear fractional differential equations and find the exact solutions. The fractional complex transform is proposed to convert a partial fractional differential equation with Jumarie's modified Riemann—Liouville derivative into its ordinary differential equation. It is shown that the considered transform and method are very efficient and powerful in solving wide classes of nonlinear fractional order equations

Fractional Order Differentiation by Integration and Error Analysis in Noisy Environment

KAUST Repository

Liu, Dayan

2015-03-31

The integer order differentiation by integration method based on the Jacobi orthogonal polynomials for noisy signals was originally introduced by Mboup, Join and Fliess. We propose to extend this method from the integer order to the fractional order to estimate the fractional order derivatives of noisy signals. Firstly, two fractional order differentiators are deduced from the Jacobi orthogonal polynomial filter, using the Riemann-Liouville and the Caputo fractional order derivative definitions respectively. Exact and simple formulae for these differentiators are given by integral expressions. Hence, they can be used for both continuous-time and discrete-time models in on-line or off-line applications. Secondly, some error bounds are provided for the corresponding estimation errors. These bounds allow to study the design parameters\\' influence. The noise error contribution due to a large class of stochastic processes is studied in discrete case. The latter shows that the differentiator based on the Caputo fractional order derivative can cope with a class of noises, whose mean value and variance functions are polynomial time-varying. Thanks to the design parameters analysis, the proposed fractional order differentiators are significantly improved by admitting a time-delay. Thirdly, in order to reduce the calculation time for on-line applications, a recursive algorithm is proposed. Finally, the proposed differentiator based on the Riemann-Liouville fractional order derivative is used to estimate the state of a fractional order system and numerical simulations illustrate the accuracy and the robustness with respect to corrupting noises.

Fractional differential equation with the fuzzy initial condition

Directory of Open Access Journals (Sweden)

Sadia Arshad

2011-02-01

Full Text Available In this paper we study the existence and uniqueness of the solution for a class of fractional differential equation with fuzzy initial value. The fractional derivatives are considered in the Riemann-Liouville sense.

A New Fractional Projective Riccati Equation Method for Solving Fractional Partial Differential Equations

International Nuclear Information System (INIS)

Feng Qing-Hua

2014-01-01

In this paper, a new fractional projective Riccati equation method is proposed to establish exact solutions for fractional partial differential equations in the sense of modified Riemann—Liouville derivative. This method can be seen as the fractional version of the known projective Riccati equation method. For illustrating the validity of this method, we apply this method to solve the space-time fractional Whitham—Broer—Kaup (WBK) equations and the nonlinear fractional Sharma—Tasso—Olever (STO) equation, and as a result, some new exact solutions for them are obtained. (general)

Spline Collocation Method for Nonlinear Multi-Term Fractional Differential Equation

OpenAIRE

Choe, Hui-Chol; Kang, Yong-Suk

2013-01-01

We study an approximation method to solve nonlinear multi-term fractional differential equations with initial conditions or boundary conditions. First, we transform the nonlinear multi-term fractional differential equations with initial conditions and boundary conditions to nonlinear fractional integral equations and consider the relations between them. We present a Spline Collocation Method and prove the existence, uniqueness and convergence of approximate solution as well as error estimatio...

Riemann-Christoffel Tensor in Differential Geometry of Fractional Order Application to Fractal Space-Time

Science.gov (United States)

Jumarie, Guy

2013-04-01

By using fractional differences, one recently proposed an alternative to the formulation of fractional differential calculus, of which the main characteristics is a new fractional Taylor series and its companion Rolle's formula which apply to non-differentiable functions. The key is that now we have at hand a differential increment of fractional order which can be manipulated exactly like in the standard Leibniz differential calculus. Briefly the fractional derivative is the quotient of fractional increments. It has been proposed that this calculus can be used to construct a differential geometry on manifold of fractional order. The present paper, on the one hand, refines the framework, and on the other hand, contributes some new results related to arc length of fractional curves, area on fractional differentiable manifold, covariant fractal derivative, Riemann-Christoffel tensor of fractional order, fractional differential equations of fractional geodesic, strip modeling of fractal space time and its relation with Lorentz transformation. The relation with Nottale's fractal space-time theory then appears in quite a natural way.

On some impulsive fractional differential equations in Banach spaces

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JinRong Wang

2010-01-01

Full Text Available This paper deals with some impulsive fractional differential equations in Banach spaces. Utilizing the Leray-Schauder fixed point theorem and the impulsive nonlinear singular version of the Gronwall inequality, the existence of \\(PC\\-mild solutions for some fractional differential equations with impulses are obtained under some easily checked conditions. At last, an example is given for demonstration.

Analytical solutions for coupling fractional partial differential equations with Dirichlet boundary conditions

Science.gov (United States)

Ding, Xiao-Li; Nieto, Juan J.

2017-11-01

In this paper, we consider the analytical solutions of coupling fractional partial differential equations (FPDEs) with Dirichlet boundary conditions on a finite domain. Firstly, the method of successive approximations is used to obtain the analytical solutions of coupling multi-term time fractional ordinary differential equations. Then, the technique of spectral representation of the fractional Laplacian operator is used to convert the coupling FPDEs to the coupling multi-term time fractional ordinary differential equations. By applying the obtained analytical solutions to the resulting multi-term time fractional ordinary differential equations, the desired analytical solutions of the coupling FPDEs are given. Our results are applied to derive the analytical solutions of some special cases to demonstrate their applicability.

Fractional order differentiation by integration: An application to fractional linear systems

KAUST Repository

Liu, Dayan

2013-02-04

In this article, we propose a robust method to compute the output of a fractional linear system defined through a linear fractional differential equation (FDE) with time-varying coefficients, where the input can be noisy. We firstly introduce an estimator of the fractional derivative of an unknown signal, which is defined by an integral formula obtained by calculating the fractional derivative of a truncated Jacobi polynomial series expansion. We then approximate the FDE by applying to each fractional derivative this formal algebraic integral estimator. Consequently, the fractional derivatives of the solution are applied on the used Jacobi polynomials and then we need to identify the unknown coefficients of the truncated series expansion of the solution. Modulating functions method is used to estimate these coefficients by solving a linear system issued from the approximated FDE and some initial conditions. A numerical result is given to confirm the reliability of the proposed method. © 2013 IFAC.

Mobility of radionuclides based on sequential extraction of soils

International Nuclear Information System (INIS)

Salbu, B.; Oughton, D.H.; Lien, H.N.; Oestby, G.; Strand, P.

1992-01-01

Since 1989, core samples of soil and vegetation from semi-natural pastures have been collected at selected sites in Norway during the growing season. The activity concentrations in soil and vegetation as well as transfer coefficients vary significantly between regions, within regions and even within sampling plot areas. In order to differentiate between mobil and inert fractions of radioactive and stable isotopes of Cs and Sr in soils, samples were extracted sequentially using agents with increasing dissolution power. The reproducibility of the sequential extraction technique is good and the data obtained seems most informative. As the distribution pattern for radioactive and stable isotopes of Cs and Sr are similar, a high degree of isotopic exchange is indicated. Based on easily leachable fractions, mobility factors are calculated. In general the mobility of 90 Sr is higher than for 137 Cs. Mobility factors are not significantly influenced by seasonal variations, but a decrease in the mobile fraction in soil with time is indicated. Mobility factors should be considered useful for modelling purposes. (au)

Approximate solution of integro-differential equation of fractional (arbitrary order

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Asma A. Elbeleze

2016-01-01

Full Text Available In the present paper, we study the integro-differential equations which are combination of differential and Fredholm–Volterra equations that have the fractional order with constant coefficients by the homotopy perturbation and the variational iteration. The fractional derivatives are described in Caputo sense. Some illustrative examples are presented.

Exp-function method for solving fractional partial differential equations.

Science.gov (United States)

Zheng, Bin

2013-01-01

We extend the Exp-function method to fractional partial differential equations in the sense of modified Riemann-Liouville derivative based on nonlinear fractional complex transformation. For illustrating the validity of this method, we apply it to the space-time fractional Fokas equation and the nonlinear fractional Sharma-Tasso-Olver (STO) equation. As a result, some new exact solutions for them are successfully established.

Fractionation study in bioleached metallurgy wastes using six-step sequential extraction.

Science.gov (United States)

Krasnodebska-Ostrega, Beata; Pałdyna, Joanna; Kowalska, Joanna; Jedynak, Łukasz; Golimowski, Jerzy

2009-08-15

The stored metallurgy wastes contain residues from ore processing operations that are characterized by relatively high concentrations of heavy metals. The bioleaching process makes use of bacteria to recover elements from industrial wastes and to decrease potential risk of environmental contamination. Wastes were treated by solutions containing bacteria. In this work, the optimized six-stage sequential extraction procedure was applied for the fractionation of Ni, Cr, Fe, Mn, Cu and Zn in iron-nickel metallurgy wastes deposited in Southern Poland (Szklary). Fractionation and total concentrations of elements in wastes before and after various bioleaching treatments were studied. Analyses of the extracts were performed by ICP-MS and FAAS. To achieve the most effective bioleaching of Zn, Cr, Ni, Cu, Mn, Fe the usage of both autotrophic and heterotrophic bacteria in sequence, combined with flushing of the residue after bioleaching is required. 80-100% of total metal concentrations were mobilized after the proposed treatment. Wastes treated according to this procedure could be deposited without any risk of environmental contamination and additionally the metals could be recovered for industrial purposes.

Local Fractional Laplace Variational Iteration Method for Solving Linear Partial Differential Equations with Local Fractional Derivative

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Ai-Min Yang

2014-01-01

Full Text Available The local fractional Laplace variational iteration method was applied to solve the linear local fractional partial differential equations. The local fractional Laplace variational iteration method is coupled by the local fractional variational iteration method and Laplace transform. The nondifferentiable approximate solutions are obtained and their graphs are also shown.

Regarding on the exact solutions for the nonlinear fractional differential equations

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Kaplan Melike

2016-01-01

Full Text Available In this work, we have considered the modified simple equation (MSE method for obtaining exact solutions of nonlinear fractional-order differential equations. The space-time fractional equal width (EW and the modified equal width (mEW equation are considered for illustrating the effectiveness of the algorithm. It has been observed that all exact solutions obtained in this paper verify the nonlinear ordinary differential equations which was obtained from nonlinear fractional-order differential equations under the terms of wave transformation relationship. The obtained results are shown graphically.

A Novel Method for Analytical Solutions of Fractional Partial Differential Equations

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Mehmet Ali Akinlar

2013-01-01

Full Text Available A new solution technique for analytical solutions of fractional partial differential equations (FPDEs is presented. The solutions are expressed as a finite sum of a vector type functional. By employing MAPLE software, it is shown that the solutions might be extended to an arbitrary degree which makes the present method not only different from the others in the literature but also quite efficient. The method is applied to special Bagley-Torvik and Diethelm fractional differential equations as well as a more general fractional differential equation.

Asymptotic behavior of solutions of linear multi-order fractional differential equation systems

OpenAIRE

Diethelm, Kai; Siegmund, Stefan; Tuan, H. T.

2017-01-01

In this paper, we investigate some aspects of the qualitative theory for multi-order fractional differential equation systems. First, we obtain a fundamental result on the existence and uniqueness for multi-order fractional differential equation systems. Next, a representation of solutions of homogeneous linear multi-order fractional differential equation systems in series form is provided. Finally, we give characteristics regarding the asymptotic behavior of solutions to some classes of line...

Analysis of Caputo Impulsive Fractional Order Differential Equations with Applications

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Lakshman Mahto

2013-01-01

Full Text Available We use Sadovskii's fixed point method to investigate the existence and uniqueness of solutions of Caputo impulsive fractional differential equations of order with one example of impulsive logistic model and few other examples as well. We also discuss Caputo impulsive fractional differential equations with finite delay. The results proven are new and compliment the existing one.

Some properties for integro-differential operator defined by a fractional formal.

Science.gov (United States)

Abdulnaby, Zainab E; Ibrahim, Rabha W; Kılıçman, Adem

2016-01-01

Recently, the study of the fractional formal (operators, polynomials and classes of special functions) has been increased. This study not only in mathematics but extended to another topics. In this effort, we investigate a generalized integro-differential operator [Formula: see text] defined by a fractional formal (fractional differential operator) and study some its geometric properties by employing it in new subclasses of analytic univalent functions.

Fractional Differential Equations in Terms of Comparison Results and Lyapunov Stability with Initial Time Difference

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Coşkun Yakar

2010-01-01

Full Text Available The qualitative behavior of a perturbed fractional-order differential equation with Caputo's derivative that differs in initial position and initial time with respect to the unperturbed fractional-order differential equation with Caputo's derivative has been investigated. We compare the classical notion of stability to the notion of initial time difference stability for fractional-order differential equations in Caputo's sense. We present a comparison result which again gives the null solution a central role in the comparison fractional-order differential equation when establishing initial time difference stability of the perturbed fractional-order differential equation with respect to the unperturbed fractional-order differential equation.

EXISTENCE AND UNIQUENESS OF SOLUTIONS TO A NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION

Institute of Scientific and Technical Information of China (English)

无

2011-01-01

The initial value problem of a nonlinear fractional differential equation is discussed in this paper. Using the nonlinear alternative of Leray-Schauder type and the contraction mapping principle,we obtain the existence and uniqueness of solutions to the fractional differential equation,which extend some results of the previous papers.

Multivariate Padé Approximation for Solving Nonlinear Partial Differential Equations of Fractional Order

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Veyis Turut

2013-01-01

Full Text Available Two tecHniques were implemented, the Adomian decomposition method (ADM and multivariate Padé approximation (MPA, for solving nonlinear partial differential equations of fractional order. The fractional derivatives are described in Caputo sense. First, the fractional differential equation has been solved and converted to power series by Adomian decomposition method (ADM, then power series solution of fractional differential equation was put into multivariate Padé series. Finally, numerical results were compared and presented in tables and figures.

Application of the Lie Symmetry Analysis for second-order fractional differential equations

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Mousa Ilie

2017-12-01

Full Text Available Obtaining analytical or numerical solution of fractional differential equations is one of the troublesome and challenging issue among mathematicians and engineers, specifically in recent years. The purpose of this paper Lie Symmetry method is developed to solve second-order fractional differential equations, based on conformable fractional derivative. Some numerical examples are presented to illustrate the proposed approach.

The Oscillation of a Class of the Fractional-Order Delay Differential Equations

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Qianli Lu

2014-01-01

Full Text Available Several oscillation results are proposed including necessary and sufficient conditions for the oscillation of fractional-order delay differential equations with constant coefficients, the sufficient or necessary and sufficient conditions for the oscillation of fractional-order delay differential equations by analysis method, and the sufficient or necessary and sufficient conditions for the oscillation of delay partial differential equation with three different boundary conditions. For this, α-exponential function which is a kind of functions that play the same role of the classical exponential functions of fractional-order derivatives is used.

A Novel Operational Matrix of Caputo Fractional Derivatives of Fibonacci Polynomials: Spectral Solutions of Fractional Differential Equations

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Waleed M. Abd-Elhameed

2016-09-01

Full Text Available Herein, two numerical algorithms for solving some linear and nonlinear fractional-order differential equations are presented and analyzed. For this purpose, a novel operational matrix of fractional-order derivatives of Fibonacci polynomials was constructed and employed along with the application of the tau and collocation spectral methods. The convergence and error analysis of the suggested Fibonacci expansion were carefully investigated. Some numerical examples with comparisons are presented to ensure the efficiency, applicability and high accuracy of the proposed algorithms. Two accurate semi-analytic polynomial solutions for linear and nonlinear fractional differential equations are the result.

Existence and Uniqueness of Solutions for Coupled Systems of Higher-Order Nonlinear Fractional Differential Equations

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Ahmad Bashir

2010-01-01

Full Text Available We study an initial value problem for a coupled Caputo type nonlinear fractional differential system of higher order. As a first problem, the nonhomogeneous terms in the coupled fractional differential system depend on the fractional derivatives of lower orders only. Then the nonhomogeneous terms in the fractional differential system are allowed to depend on the unknown functions together with the fractional derivative of lower orders. Our method of analysis is based on the reduction of the given system to an equivalent system of integral equations. Applying the nonlinear alternative of Leray-Schauder, we prove the existence of solutions of the fractional differential system. The uniqueness of solutions of the fractional differential system is established by using the Banach contraction principle. An illustrative example is also presented.

A non-differentiable solution for the local fractional telegraph equation

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Li Jie

2017-01-01

Full Text Available In this paper, we consider the linear telegraph equations with local fractional derivative. The local fractional Laplace series expansion method is used to handle the local fractional telegraph equation. The analytical solution with the non-differentiable graphs is discussed in detail. The proposed method is efficient and accurate.

A Variable Order Fractional Differential-Based Texture Enhancement Algorithm with Application in Medical Imaging.

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Qiang Yu

Full Text Available Texture enhancement is one of the most important techniques in digital image processing and plays an essential role in medical imaging since textures discriminate information. Most image texture enhancement techniques use classical integral order differential mask operators or fractional differential mask operators using fixed fractional order. These masks can produce excessive enhancement of low spatial frequency content, insufficient enhancement of large spatial frequency content, and retention of high spatial frequency noise. To improve upon existing approaches of texture enhancement, we derive an improved Variable Order Fractional Centered Difference (VOFCD scheme which dynamically adjusts the fractional differential order instead of fixing it. The new VOFCD technique is based on the second order Riesz fractional differential operator using a Lagrange 3-point interpolation formula, for both grey scale and colour image enhancement. We then use this method to enhance photographs and a set of medical images related to patients with stroke and Parkinson's disease. The experiments show that our improved fractional differential mask has a higher signal to noise ratio value than the other fractional differential mask operators. Based on the corresponding quantitative analysis we conclude that the new method offers a superior texture enhancement over existing methods.

Exact Solutions for Fractional Differential-Difference Equations by an Extended Riccati Sub-ODE Method

International Nuclear Information System (INIS)

Feng Qinghua

2013-01-01

In this paper, an extended Riccati sub-ODE method is proposed to establish new exact solutions for fractional differential-difference equations in the sense of modified Riemann—Liouville derivative. By a fractional complex transformation, a given fractional differential-difference equation can be turned into another differential-difference equation of integer order. The validity of the method is illustrated by applying it to solve the fractional Hybrid lattice equation and the fractional relativistic Toda lattice system. As a result, some new exact solutions including hyperbolic function solutions, trigonometric function solutions and rational solutions are established. (general)

Integro-differential equations of fractional order with nonlocal fractional boundary conditions associated with financial asset model

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Bashir Ahmad

2013-02-01

Full Text Available In this article, we discuss the existence of solutions for a boundary-value problem of integro-differential equations of fractional order with nonlocal fractional boundary conditions by means of some standard tools of fixed point theory. Our problem describes a more general form of fractional stochastic dynamic model for financial asset. An illustrative example is also presented.

A multi-domain spectral method for time-fractional differential equations

Science.gov (United States)

Chen, Feng; Xu, Qinwu; Hesthaven, Jan S.

2015-07-01

This paper proposes an approach for high-order time integration within a multi-domain setting for time-fractional differential equations. Since the kernel is singular or nearly singular, two main difficulties arise after the domain decomposition: how to properly account for the history/memory part and how to perform the integration accurately. To address these issues, we propose a novel hybrid approach for the numerical integration based on the combination of three-term-recurrence relations of Jacobi polynomials and high-order Gauss quadrature. The different approximations used in the hybrid approach are justified theoretically and through numerical examples. Based on this, we propose a new multi-domain spectral method for high-order accurate time integrations and study its stability properties by identifying the method as a generalized linear method. Numerical experiments confirm hp-convergence for both time-fractional differential equations and time-fractional partial differential equations.

Application of the principal fractional meta-trigonometric functions for the solution of linear commensurate-order time-invariant fractional differential equations.

Science.gov (United States)

Lorenzo, C F; Hartley, T T; Malti, R

2013-05-13

A new and simplified method for the solution of linear constant coefficient fractional differential equations of any commensurate order is presented. The solutions are based on the R-function and on specialized Laplace transform pairs derived from the principal fractional meta-trigonometric functions. The new method simplifies the solution of such fractional differential equations and presents the solutions in the form of real functions as opposed to fractional complex exponential functions, and thus is directly applicable to real-world physics.

Stability analysis of a class of fractional delay differential equations

Indian Academy of Sciences (India)

In this paper we analyse stability of nonlinear fractional order delay differential equations of the form D y ( t ) = a f ( y ( t − ) ) − by ( t ) , where D is a Caputo fractional derivative of order 0 < ≤ 1. We describe stability regions using critical curves. To explain the proposed theory, we discuss fractional order logistic ...

Stability analysis of a class of fractional delay differential equations

Indian Academy of Sciences (India)

Abstract. In this paper we analyse stability of nonlinear fractional order delay differential equa- tions of the form Dα y(t) = af (y(t − τ )) − by(t), where Dα is a Caputo fractional derivative of order 0 < α ≤ 1. We describe stability regions using critical curves. To explain the proposed theory, we discuss fractional order logistic ...

Boundary value problem for Caputo-Hadamard fractional differential equations

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Yacine Arioua

2017-09-01

Full Text Available The aim of this work is to study the existence and uniqueness solutions for boundary value problem of nonlinear fractional differential equations with Caputo-Hadamard derivative in bounded domain. We used the standard and Krasnoselskii's fixed point theorems. Some new results of existence and uniqueness solutions for Caputo-Hadamard fractional equations are obtained.

The reproducibility and variability of sequential left ventricular ejection fraction measurements by the nuclear stethoscope

International Nuclear Information System (INIS)

Kurata, Chinori; Hayashi, Hideharu; Kobayashi, Akira; Yamazaki, Noboru

1986-01-01

We evaluated the reproducibility and variability of sequential left ventricular ejection fraction (LVEF) measurements by the nuclear stethoscope in 72 patients. The group as a whole demonstrated excellent reproducibility (r = 0.96). However, repeat LVEF measurements by the nuclear stethoscope at 5-minute interval showed around 9 % absolute difference, at 95 % confidence levels, from one measurement to the next. The finding indicates that a change in LVEF greater than 9 % is necessary for determining an acute effect of an intervention in individual cases. (author)

Impact of sequential proton density fat fraction for quantification of hepatic steatosis in nonalcoholic fatty liver disease.

Science.gov (United States)

Idilman, Ilkay S; Keskin, Onur; Elhan, Atilla Halil; Idilman, Ramazan; Karcaaltincaba, Musturay

2014-05-01

To determine the utility of sequential MRI-estimated proton density fat fraction (MRI-PDFF) for quantification of the longitudinal changes in liver fat content in individuals with nonalcoholic fatty liver disease (NAFLD). A total of 18 consecutive individuals (M/F: 10/8, mean age: 47.7±9.8 years) diagnosed with NAFLD, who underwent sequential PDFF calculations for the quantification of hepatic steatosis at two different time points, were included in the study. All patients underwent T1-independent volumetric multi-echo gradient-echo imaging with T2* correction and spectral fat modeling. A close correlation for quantification of hepatic steatosis between the initial MRI-PDFF and liver biopsy was observed (rs=0.758, phepatic steatosis. The changes in serum ALT levels significantly reflected changes in MRI-PDFF in patients with NAFLD.

A Novel Method for Analytical Solutions of Fractional Partial Differential Equations

OpenAIRE

Mehmet Ali Akinlar; Muhammet Kurulay

2013-01-01

A new solution technique for analytical solutions of fractional partial differential equations (FPDEs) is presented. The solutions are expressed as a finite sum of a vector type functional. By employing MAPLE software, it is shown that the solutions might be extended to an arbitrary degree which makes the present method not only different from the others in the literature but also quite efficient. The method is applied to special Bagley-Torvik and Diethelm fractional differential equations as...

Lie Group Classifications and Non-differentiable Solutions for Time-Fractional Burgers Equation

International Nuclear Information System (INIS)

Wu Guocheng

2011-01-01

Lie group method provides an efficient tool to solve nonlinear partial differential equations. This paper suggests Lie group method for fractional partial differential equations. A time-fractional Burgers equation is used as an example to illustrate the effectiveness of the Lie group method and some classes of exact solutions are obtained. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

Stationarity-conservation laws for fractional differential equations with variable coefficients

International Nuclear Information System (INIS)

Klimek, Malgorzata

2002-01-01

In this paper, we study linear fractional differential equations with variable coefficients. It is shown that, by assuming some conditions for the coefficients, the stationarity-conservation laws can be derived. The area where these are valid is restricted by the asymptotic properties of solutions of the respective equation. Applications of the proposed procedure include the fractional Fokker-Planck equation in (1+1)- and (d+1)-dimensional space and the fractional Klein-Kramers equation. (author)

Stationarity-conservation laws for fractional differential equations with variable coefficients

Energy Technology Data Exchange (ETDEWEB)

Klimek, Malgorzata [Institute of Mathematics and Computer Science, Technical University of Czestochowa, Czestochowa (Poland)

2002-08-09

In this paper, we study linear fractional differential equations with variable coefficients. It is shown that, by assuming some conditions for the coefficients, the stationarity-conservation laws can be derived. The area where these are valid is restricted by the asymptotic properties of solutions of the respective equation. Applications of the proposed procedure include the fractional Fokker-Planck equation in (1+1)- and (d+1)-dimensional space and the fractional Klein-Kramers equation. (author)

Analytical approach to linear fractional partial differential equations arising in fluid mechanics

International Nuclear Information System (INIS)

Momani, Shaher; Odibat, Zaid

2006-01-01

In this Letter, we implement relatively new analytical techniques, the variational iteration method and the Adomian decomposition method, for solving linear fractional partial differential equations arising in fluid mechanics. The fractional derivatives are described in the Caputo sense. The two methods in applied mathematics can be used as alternative methods for obtaining analytic and approximate solutions for different types of fractional differential equations. In these methods, the solution takes the form of a convergent series with easily computable components. The corresponding solutions of the integer order equations are found to follow as special cases of those of fractional order equations. Some numerical examples are presented to illustrate the efficiency and reliability of the two methods

Higher order multi-term time-fractional partial differential equations involving Caputo-Fabrizio derivative

OpenAIRE

Erkinjon Karimov; Sardor Pirnafasov

2017-01-01

In this work we discuss higher order multi-term partial differential equation (PDE) with the Caputo-Fabrizio fractional derivative in time. Using method of separation of variables, we reduce fractional order partial differential equation to the integer order. We represent explicit solution of formulated problem in particular case by Fourier series.

Solution of fractional-order differential equations based on the operational matrices of new fractional Bernstein functions

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M.H.T. Alshbool

2017-01-01

Full Text Available An algorithm for approximating solutions to fractional differential equations (FDEs in a modified new Bernstein polynomial basis is introduced. Writing x→xα(0<α<1 in the operational matrices of Bernstein polynomials, the fractional Bernstein polynomials are obtained and then transformed into matrix form. Furthermore, using Caputo fractional derivative, the matrix form of the fractional derivative is constructed for the fractional Bernstein matrices. We convert each term of the problem to the matrix form by means of fractional Bernstein matrices. A basic matrix equation which corresponds to a system of fractional equations is utilized, and a new system of nonlinear algebraic equations is obtained. The method is given with some priori error estimate. By using the residual correction procedure, the absolute error can be estimated. Illustrative examples are included to demonstrate the validity and applicability of the presented technique.

Solving Fuzzy Fractional Differential Equations Using Zadeh's Extension Principle

Science.gov (United States)

Ahmad, M. Z.; Hasan, M. K.; Abbasbandy, S.

2013-01-01

We study a fuzzy fractional differential equation (FFDE) and present its solution using Zadeh's extension principle. The proposed study extends the case of fuzzy differential equations of integer order. We also propose a numerical method to approximate the solution of FFDEs. To solve nonlinear problems, the proposed numerical method is then incorporated into an unconstrained optimisation technique. Several numerical examples are provided. PMID:24082853

The convergence of the order sequence and the solution function sequence on fractional partial differential equation

Science.gov (United States)

Rusyaman, E.; Parmikanti, K.; Chaerani, D.; Asefan; Irianingsih, I.

2018-03-01

One of the application of fractional ordinary differential equation is related to the viscoelasticity, i.e., a correlation between the viscosity of fluids and the elasticity of solids. If the solution function develops into function with two or more variables, then its differential equation must be changed into fractional partial differential equation. As the preliminary study for two variables viscoelasticity problem, this paper discusses about convergence analysis of function sequence which is the solution of the homogenous fractional partial differential equation. The method used to solve the problem is Homotopy Analysis Method. The results show that if given two real number sequences (αn) and (βn) which converge to α and β respectively, then the solution function sequences of fractional partial differential equation with order (αn, βn) will also converge to the solution function of fractional partial differential equation with order (α, β).

A numerical technique for solving fractional optimal control problems and fractional Riccati differential equations

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F. Ghomanjani

2016-10-01

Full Text Available In the present paper, we apply the Bezier curves method for solving fractional optimal control problems (OCPs and fractional Riccati differential equations. The main advantage of this method is that it can reduce the error of the approximate solutions. Hence, the solutions obtained using the Bezier curve method give good approximations. Some numerical examples are provided to confirm the accuracy of the proposed method. All of the numerical computations have been performed on a PC using several programs written in MAPLE 13.

Fractionation of potentially toxic elements in urban soils from five European cities by means of a harmonised sequential extraction procedure

International Nuclear Information System (INIS)

Davidson, Christine M.; Urquhart, Graham J.; Ajmone-Marsan, Franco; Biasioli, Mattia; Costa Duarte, Armando da; Diaz-Barrientos, Encarnacion; Grcman, Helena; Hossack, Iain; Hursthouse, Andrew S.; Madrid, Luis; Rodrigues, Sonia; Zupan, Marko

2006-01-01

The revised (four-step) BCR sequential extraction procedure has been applied to fractionate the chromium, copper, iron, manganese, nickel, lead and zinc contents in urban soil samples from public-access areas in five European cities. A preliminary inter-laboratory comparison was conducted and showed that data obtained by different laboratories participating in the study were sufficiently harmonious for comparisons to be made between cities and land types (e.g. parks, roadside, riverbanks, etc.). Analyte recoveries by sequential extraction, with respect to direct aqua regia digestion, were generally acceptable (100 ± 15%). Iron, nickel and, at most sites, chromium were found mainly in association with the residual phase of the soil matrix. Copper was present in the reducible, oxidisable and residual fractions, whilst zinc was found in all four sequential extracts. Manganese was strongly associated with reducible material as, in some cities, was lead. This is of concern because high lead concentrations were present in some soils (>500 mg kg -1 ) and the potential exists for remobilisation under reducing conditions. As would be expected, extractable metal contents were generally highest in older, more heavily industrialised cities. Copper, lead and zinc showed marked (and often correlated) variations in concentrations between sites within the same city whereas manganese and, especially, iron, did not. No overall relationships were, however, found between analyte concentrations and land use, nor between analyte partitioning and land use

On the Asymptotic Behavior of Positive Solutions of Certain Fractional Differential Equations

OpenAIRE

Said R. Grace

2015-01-01

This paper deals with the asymptotic behavior of positive solutions of certain forced fractional differential equations of the form DcαCyt=et+ft, xt, c>1, α∈0,1, where yt=atx′t′, c0=y(c)/Γ(1) =yc, and c0 is a real constant. From the obtained results, we derive a technique which can be applied to some related fractional differential equations.

Solving Nonlinear Fractional Differential Equation by Generalized Mittag-Leffler Function Method

Science.gov (United States)

Arafa, A. A. M.; Rida, S. Z.; Mohammadein, A. A.; Ali, H. M.

2013-06-01

In this paper, we use Mittag—Leffler function method for solving some nonlinear fractional differential equations. A new solution is constructed in power series. The fractional derivatives are described by Caputo's sense. To illustrate the reliability of the method, some examples are provided.

Fractional Stochastic Differential Equations Satisfying Fluctuation-Dissipation Theorem

Science.gov (United States)

Li, Lei; Liu, Jian-Guo; Lu, Jianfeng

2017-10-01

We propose in this work a fractional stochastic differential equation (FSDE) model consistent with the over-damped limit of the generalized Langevin equation model. As a result of the `fluctuation-dissipation theorem', the differential equations driven by fractional Brownian noise to model memory effects should be paired with Caputo derivatives, and this FSDE model should be understood in an integral form. We establish the existence of strong solutions for such equations and discuss the ergodicity and convergence to Gibbs measure. In the linear forcing regime, we show rigorously the algebraic convergence to Gibbs measure when the `fluctuation-dissipation theorem' is satisfied, and this verifies that satisfying `fluctuation-dissipation theorem' indeed leads to the correct physical behavior. We further discuss possible approaches to analyze the ergodicity and convergence to Gibbs measure in the nonlinear forcing regime, while leave the rigorous analysis for future works. The FSDE model proposed is suitable for systems in contact with heat bath with power-law kernel and subdiffusion behaviors.

Higher order multi-term time-fractional partial differential equations involving Caputo-Fabrizio derivative

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Erkinjon Karimov

2017-10-01

Full Text Available In this work we discuss higher order multi-term partial differential equation (PDE with the Caputo-Fabrizio fractional derivative in time. Using method of separation of variables, we reduce fractional order partial differential equation to the integer order. We represent explicit solution of formulated problem in particular case by Fourier series.

Efficacy and toxicity of conventionally fractionated pelvic radiation with a hypo fractionated simultaneous versus conventionally fractionated sequential boost for patients with high-risk prostate cancer

International Nuclear Information System (INIS)

McDonald, Andrew M.; Jacob, Rojymon; Dobelbower, Michael C.; Kim, Robert Y.; Fiveash, John B.

2013-01-01

Purpose: To determine if high-risk prostate cancer responds differently to hypo fractionation. Material and methods: One hundred and fifty-seven men with NCCN high-risk (T3, PSA 20, or Gleason 8) clinically localized prostate cancer treated between 1998 and 2010 met the inclusion criteria for the analysis. Eighty-two were treated with conventional WPRT with a conventionally fractionated sequential boost to the prostate (cRT), with the prostate receiving 75-77 Gy in 1.8 - 2.0 Gy fractions. Seventy-five were treated with pelvic IMRT with a hypo fractionated simultaneous boost to the prostate (hRT), with the prostate receiving 70 Gy in 2.5 Gy fractions. The dose to the pelvic lymph nodes was 45 Gy in the cRT group and 50.4 Gy in the hRT group, both at 1.8 Gy per fraction. Ninety-two percent received neoadjuvant hormonal ablation therapy, typically beginning two months prior to the start of RT. Results: Median follow-up was 6.5 years for men receiving cRT and 3.7 years for those receiving hRT. The actuarial rate of biochemical control at four years was 88% for cRT and 94% for hRT (p=0.82). The rates of early rectal and urinary grade ≥2 toxicities were 35% (29 of 82) and 49% (40 of 82) for the cRT group and 36% (27 of 75) and 44% (33 of 75) for the hRT group. The actuarial rate of late grade 2 rectal toxicity at four years was 25% for the cRT group and 13% for the hRT group (p=0.037). The rate of late grade 3 rectal complications was 4% (3 of 82) for patients receiving cRT and 1% (1 of 75) for patients receiving hRT. Conclusion: Initial follow-up indicates equivalent biochemical control between regimens. Patients receiving hRT experienced fewer late rectal complications

The analysis of fractional differential equations an application-oriented exposition using differential operators of Caputo type

CERN Document Server

Diethelm, Kai

2010-01-01

Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. Some 100 years later, engineers and physicists have found applications for these concepts in their areas. However there has traditionally been little interaction between these two communities. In particular, typical mathematical works provide extensive findings on aspects with comparatively little significance in applications, and the engineering literature often lacks mathematical detail and precision. This book bridges the gap between the two communities. It concentrates on the class of fractional derivatives most important in applications, the Caputo operators, and provides a self-contained, thorough and mathematically rigorous study of their properties and of the corresponding differential equations. The text is a useful tool for mathematicians and researchers from the applied sciences alike. It can also be used as a basis for teaching graduate courses on fractional differential equations.

Computational Challenge of Fractional Differential Equations and the Potential Solutions: A Survey

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Chunye Gong

2015-01-01

Full Text Available We present a survey of fractional differential equations and in particular of the computational cost for their numerical solutions from the view of computer science. The computational complexities of time fractional, space fractional, and space-time fractional equations are O(N2M, O(NM2, and O(NM(M + N compared with O(MN for the classical partial differential equations with finite difference methods, where M, N are the number of space grid points and time steps. The potential solutions for this challenge include, but are not limited to, parallel computing, memory access optimization (fractional precomputing operator, short memory principle, fast Fourier transform (FFT based solutions, alternating direction implicit method, multigrid method, and preconditioner technology. The relationships of these solutions for both space fractional derivative and time fractional derivative are discussed. The authors pointed out that the technologies of parallel computing should be regarded as a basic method to overcome this challenge, and some attention should be paid to the fractional killer applications, high performance iteration methods, high order schemes, and Monte Carlo methods. Since the computation of fractional equations with high dimension and variable order is even heavier, the researchers from the area of mathematics and computer science have opportunity to invent cornerstones in the area of fractional calculus.

New Solutions of Three Nonlinear Space- and Time-Fractional Partial Differential Equations in Mathematical Physics

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Yao Ruo-Xia; Wang Wei; Chen Ting-Hua

2014-01-01

Motivated by the widely used ansätz method and starting from the modified Riemann—Liouville derivative together with a fractional complex transformation that can be utilized to transform nonlinear fractional partial differential equations to nonlinear ordinary differential equations, new types of exact traveling wave solutions to three important nonlinear space- and time-fractional partial differential equations are obtained simultaneously in terms of solutions of a Riccati equation. The results are new and first reported in this paper. (general)

Numerical solution of distributed order fractional differential equations

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Katsikadelis, John T.

2014-02-01

In this paper a method for the numerical solution of distributed order FDEs (fractional differential equations) of a general form is presented. The method applies to both linear and nonlinear equations. The Caputo type fractional derivative is employed. The distributed order FDE is approximated with a multi-term FDE, which is then solved by adjusting appropriately the numerical method developed for multi-term FDEs by Katsikadelis. Several example equations are solved and the response of mechanical systems described by such equations is studied. The convergence and the accuracy of the method for linear and nonlinear equations are demonstrated through well corroborated numerical results.

Bright and dark soliton solutions for some nonlinear fractional differential equations

International Nuclear Information System (INIS)

Guner, Ozkan; Bekir, Ahmet

2016-01-01

In this work, we propose a new approach, namely ansatz method, for solving fractional differential equations based on a fractional complex transform and apply it to the nonlinear partial space–time fractional modified Benjamin–Bona–Mahoney (mBBM) equation, the time fractional mKdV equation and the nonlinear fractional Zoomeron equation which gives rise to some new exact solutions. The physical parameters in the soliton solutions: amplitude, inverse width, free parameters and velocity are obtained as functions of the dependent model coefficients. This method is suitable and more powerful for solving other kinds of nonlinear fractional PDEs arising in mathematical physics. Since the fractional derivatives are described in the modified Riemann–Liouville sense. (paper)

Arsenic fractionation in agricultural soil using an automated three-step sequential extraction method coupled to hydride generation-atomic fluorescence spectrometry

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Rosas-Castor, J.M. [Universidad Autónoma de Nuevo León, UANL, Facultad de Ciencias Químicas, Cd. Universitaria, San Nicolás de los Garza, Nuevo León, C.P. 66451 Nuevo León (Mexico); Group of Analytical Chemistry, Automation and Environment, University of Balearic Islands, Cra. Valldemossa km 7.5, 07122 Palma de Mallorca (Spain); Portugal, L.; Ferrer, L. [Group of Analytical Chemistry, Automation and Environment, University of Balearic Islands, Cra. Valldemossa km 7.5, 07122 Palma de Mallorca (Spain); Guzmán-Mar, J.L.; Hernández-Ramírez, A. [Universidad Autónoma de Nuevo León, UANL, Facultad de Ciencias Químicas, Cd. Universitaria, San Nicolás de los Garza, Nuevo León, C.P. 66451 Nuevo León (Mexico); Cerdà, V. [Group of Analytical Chemistry, Automation and Environment, University of Balearic Islands, Cra. Valldemossa km 7.5, 07122 Palma de Mallorca (Spain); Hinojosa-Reyes, L., E-mail: laura.hinojosary@uanl.edu.mx [Universidad Autónoma de Nuevo León, UANL, Facultad de Ciencias Químicas, Cd. Universitaria, San Nicolás de los Garza, Nuevo León, C.P. 66451 Nuevo León (Mexico)

2015-05-18

Highlights: • A fully automated flow-based modified-BCR extraction method was developed to evaluate the extractable As of soil. • The MSFIA–HG-AFS system included an UV photo-oxidation step for organic species degradation. • The accuracy and precision of the proposed method were found satisfactory. • The time analysis can be reduced up to eight times by using the proposed flow-based BCR method. • The labile As (F1 + F2) was <50% of total As in soil samples from As-contaminated-mining zones. - Abstract: A fully automated modified three-step BCR flow-through sequential extraction method was developed for the fractionation of the arsenic (As) content from agricultural soil based on a multi-syringe flow injection analysis (MSFIA) system coupled to hydride generation-atomic fluorescence spectrometry (HG-AFS). Critical parameters that affect the performance of the automated system were optimized by exploiting a multivariate approach using a Doehlert design. The validation of the flow-based modified-BCR method was carried out by comparison with the conventional BCR method. Thus, the total As content was determined in the following three fractions: fraction 1 (F1), the acid-soluble or interchangeable fraction; fraction 2 (F2), the reducible fraction; and fraction 3 (F3), the oxidizable fraction. The limits of detection (LOD) were 4.0, 3.4, and 23.6 μg L{sup −1} for F1, F2, and F3, respectively. A wide working concentration range was obtained for the analysis of each fraction, i.e., 0.013–0.800, 0.011–0.900 and 0.079–1.400 mg L{sup −1} for F1, F2, and F3, respectively. The precision of the automated MSFIA–HG-AFS system, expressed as the relative standard deviation (RSD), was evaluated for a 200 μg L{sup −1} As standard solution, and RSD values between 5 and 8% were achieved for the three BCR fractions. The new modified three-step BCR flow-based sequential extraction method was satisfactorily applied for arsenic fractionation in real agricultural

Analytical solutions of time-fractional models for homogeneous Gardner equation and non-homogeneous differential equations

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Olaniyi Samuel Iyiola

2014-09-01

Full Text Available In this paper, we obtain analytical solutions of homogeneous time-fractional Gardner equation and non-homogeneous time-fractional models (including Buck-master equation using q-Homotopy Analysis Method (q-HAM. Our work displays the elegant nature of the application of q-HAM not only to solve homogeneous non-linear fractional differential equations but also to solve the non-homogeneous fractional differential equations. The presence of the auxiliary parameter h helps in an effective way to obtain better approximation comparable to exact solutions. The fraction-factor in this method gives it an edge over other existing analytical methods for non-linear differential equations. Comparisons are made upon the existence of exact solutions to these models. The analysis shows that our analytical solutions converge very rapidly to the exact solutions.

The G′G-expansion method using modified Riemann–Liouville derivative for some space-time fractional differential equations

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Ahmet Bekir

2014-09-01

Full Text Available In this paper, the fractional partial differential equations are defined by modified Riemann–Liouville fractional derivative. With the help of fractional derivative and traveling wave transformation, these equations can be converted into the nonlinear nonfractional ordinary differential equations. Then G′G-expansion method is applied to obtain exact solutions of the space-time fractional Burgers equation, the space-time fractional KdV-Burgers equation and the space-time fractional coupled Burgers’ equations. As a result, many exact solutions are obtained including hyperbolic function solutions, trigonometric function solutions and rational solutions. These results reveal that the proposed method is very effective and simple in performing a solution to the fractional partial differential equation.

New numerical approximation for solving fractional delay differential equations of variable order using artificial neural networks

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Zúñiga-Aguilar, C. J.; Coronel-Escamilla, A.; Gómez-Aguilar, J. F.; Alvarado-Martínez, V. M.; Romero-Ugalde, H. M.

2018-02-01

In this paper, we approximate the solution of fractional differential equations with delay using a new approach based on artificial neural networks. We consider fractional differential equations of variable order with the Mittag-Leffler kernel in the Liouville-Caputo sense. With this new neural network approach, an approximate solution of the fractional delay differential equation is obtained. Synaptic weights are optimized using the Levenberg-Marquardt algorithm. The neural network effectiveness and applicability were validated by solving different types of fractional delay differential equations, linear systems with delay, nonlinear systems with delay and a system of differential equations, for instance, the Newton-Leipnik oscillator. The solution of the neural network was compared with the analytical solutions and the numerical simulations obtained through the Adams-Bashforth-Moulton method. To show the effectiveness of the proposed neural network, different performance indices were calculated.

ALMOST AUTOMORPHIC MILD SOLUTIONS TO SOME FRACTIONAL DELAY DIFFERENTIAL EQUATIONS

Institute of Scientific and Technical Information of China (English)

无

2012-01-01

In this paper,a new and general existence and uniqueness theorem of almost automorphic mild solutions is obtained for some fractional delay differential equations,using sectorial operators and the Banach contraction principle.

Numerical solution for multi-term fractional (arbitrary) orders differential equations

OpenAIRE

El-Sayed, A. M. A.; El-Mesiry, A. E. M.; El-Saka, H. A. A.

2004-01-01

Our main concern here is to give a numerical scheme to solve a nonlinear multi-term fractional (arbitrary) orders differential equation. Some results concerning the existence and uniqueness have been also obtained.

Conservation laws for certain time fractional nonlinear systems of partial differential equations

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Singla, Komal; Gupta, R. K.

2017-12-01

In this study, an extension of the concept of nonlinear self-adjointness and Noether operators is proposed for calculating conserved vectors of the time fractional nonlinear systems of partial differential equations. In our recent work (J Math Phys 2016; 57: 101504), by proposing the symmetry approach for time fractional systems, the Lie symmetries for some fractional nonlinear systems have been derived. In this paper, the obtained infinitesimal generators are used to find conservation laws for the corresponding fractional systems.

Multiple positive solutions to a coupled systems of nonlinear fractional differential equations.

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Shah, Kamal; Khan, Rahmat Ali

2016-01-01

In this article, we study existence, uniqueness and nonexistence of positive solution to a highly nonlinear coupled system of fractional order differential equations. Necessary and sufficient conditions for the existence and uniqueness of positive solution are developed by using Perov's fixed point theorem for the considered problem. Further, we also established sufficient conditions for existence of multiplicity results for positive solutions. Also, we developed some conditions under which the considered coupled system of fractional order differential equations has no positive solution. Appropriate examples are also provided which demonstrate our results.

On Comparison Theorems for Conformable Fractional Differential Equations

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Mehmet Zeki Sarikaya

2016-10-01

Full Text Available In this paper the more general comparison theorems for conformable fractional differential equations is proposed and tested. Thus we prove some inequalities for conformable integrals by using the generalization of Sturm's separation and Sturm's comparison theorems. The results presented here would provide generalizations of those given in earlier works. The numerical example is also presented to verify the proposed theorem.

Differential isospin-fractionation in dilute asymmetric nuclear matter

International Nuclear Information System (INIS)

Li Baoan; Chen Liewen; Ma Hongru; Xu Jun; Yong Gaochan

2007-01-01

The differential isospin-fractionation (IsoF) during the liquid-gas phase transition in dilute asymmetric nuclear matter is studied as a function of nucleon momentum. Within a self-consistent thermal model it is shown that the neutron/proton ratio of the gas phase becomes smaller than that of the liquid phase for energetic nucleons, although the gas phase is overall more neutron-rich. Clear indications of the differential IsoF consistent with the thermal model predictions are demonstrated within a transport model for heavy-ion reactions. Future comparisons with experimental data will allow us to extract critical information about the momentum dependence of the isovector strong interaction

Existence of solutions to boundary value problem of fractional differential equations with impulsive

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Weihua JIANG

2016-12-01

Full Text Available In order to solve the boundary value problem of fractional impulsive differential equations with countable impulses and integral boundary conditions on the half line, the existence of solutions to the boundary problem is specifically studied. By defining suitable Banach spaces, norms and operators, using the properties of fractional calculus and applying the contraction mapping principle and Krasnoselskii's fixed point theorem, the existence of solutions for the boundary value problem of fractional impulsive differential equations with countable impulses and integral boundary conditions on the half line is proved, and examples are given to illustrate the existence of solutions to this kind of equation boundary value problems.

A Solution to the Fundamental Linear Fractional Order Differential Equation

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Hartley, Tom T.; Lorenzo, Carl F.

1998-01-01

This paper provides a solution to the fundamental linear fractional order differential equation, namely, (sub c)d(sup q, sub t) + ax(t) = bu(t). The impulse response solution is shown to be a series, named the F-function, which generalizes the normal exponential function. The F-function provides the basis for a qth order "fractional pole". Complex plane behavior is elucidated and a simple example, the inductor terminated semi- infinite lossy line, is used to demonstrate the theory.

A Predictor-Corrector Approach for the Numerical Solution of Fractional Differential Equations

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Diethelm, Kai; Ford, Neville J.; Freed, Alan D.; Gray, Hugh R. (Technical Monitor)

2002-01-01

We discuss an Adams-type predictor-corrector method for the numerical solution of fractional differential equations. The method may be used both for linear and for nonlinear problems, and it may be extended to multi-term equations (involving more than one differential operator) too.

Fractional Order Stochastic Differential Equation with Application in European Option Pricing

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Qing Li

2014-01-01

Full Text Available Memory effect is an important phenomenon in financial systems, and a number of research works have been carried out to study the long memory in the financial markets. In recent years, fractional order ordinary differential equation is used as an effective instrument for describing the memory effect in complex systems. In this paper, we establish a fractional order stochastic differential equation (FSDE model to describe the effect of trend memory in financial pricing. We, then, derive a European option pricing formula based on the FSDE model and prove the existence of the trend memory (i.e., the mean value function in the option pricing formula when the Hurst index is between 0.5 and 1. In addition, we make a comparison analysis between our proposed model, the classic Black-Scholes model, and the stochastic model with fractional Brownian motion. Numerical results suggest that our model leads to more accurate and lower standard deviation in the empirical study.

A modification of \\mathsf {WKB} method for fractional differential operators of Schrödinger's type

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Sayevand, K.; Pichaghchi, K.

2017-09-01

In this paper, we were concerned with the description of the singularly perturbed differential equations within the scope of fractional calculus. However, we shall note that one of the main methods used to solve these problems is the so-called WKB method. We should mention that this was not achievable via the existing fractional derivative definitions, because they do not obey the chain rule. In order to accommodate the WKB to the scope of fractional derivative, we proposed a relatively new derivative called the local fractional derivative. By use of properties of local fractional derivative, we extend the WKB method in the scope of the fractional differential equation. By means of this extension, the WKB analysis based on the Borel resummation, for fractional differential operators of WKB type are investigated. The convergence and the Mittag-Leffler stability of the proposed approach is proven. The obtained results are in excellent agreement with the existing ones in open literature and it is shown that the present approach is very effective and accurate. Furthermore, we are mainly interested to construct the solution of fractional Schrödinger equation in the Mittag-Leffler form and how it leads naturally to this semi-classical approximation namely modified WKB.

General solution of the Bagley-Torvik equation with fractional-order derivative

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Wang, Z. H.; Wang, X.

2010-05-01

This paper investigates the general solution of the Bagley-Torvik equation with 1/2-order derivative or 3/2-order derivative. This fractional-order differential equation is changed into a sequential fractional-order differential equation (SFDE) with constant coefficients. Then the general solution of the SFDE is expressed as the linear combination of fundamental solutions that are in terms of α-exponential functions, a kind of functions that play the same role of the classical exponential function. Because the number of fundamental solutions of the SFDE is greater than 2, the general solution of the SFDE depends on more than two free (independent) constants. This paper shows that the general solution of the Bagley-Torvik equation involves actually two free constants only, and it can be determined fully by the initial displacement and initial velocity.

Solution of Fractional Partial Differential Equations in Fluid Mechanics by Extension of Some Iterative Method

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A. A. Hemeda

2013-01-01

Full Text Available An extension of the so-called new iterative method (NIM has been used to handle linear and nonlinear fractional partial differential equations. The main property of the method lies in its flexibility and ability to solve nonlinear equations accurately and conveniently. Therefore, a general framework of the NIM is presented for analytical treatment of fractional partial differential equations in fluid mechanics. The fractional derivatives are described in the Caputo sense. Numerical illustrations that include the fractional wave equation, fractional Burgers equation, fractional KdV equation, fractional Klein-Gordon equation, and fractional Boussinesq-like equation are investigated to show the pertinent features of the technique. Comparison of the results obtained by the NIM with those obtained by both Adomian decomposition method (ADM and the variational iteration method (VIM reveals that the NIM is very effective and convenient. The basic idea described in this paper is expected to be further employed to solve other similar linear and nonlinear problems in fractional calculus.

Asymptotic behavior of solutions of forced fractional differential equations

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Said Grace

2016-09-01

where $y(t=\\left( a(tx^{\\prime }(t\\right ^{\\prime }$, $c_{0}=\\frac{y(c}{\\Gamma (1}=y(c$, and $c_{0}$ is a real constant. The technique used in obtaining their results will apply to related fractional differential equations with Caputo derivatives of any order. Examples illustrate the results obtained in this paper.

Numerical solutions of multi-order fractional differential equations by Boubaker polynomials

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Bolandtalat A.

2016-01-01

Full Text Available In this paper, we have applied a numerical method based on Boubaker polynomials to obtain approximate numerical solutions of multi-order fractional differential equations. We obtain an operational matrix of fractional integration based on Boubaker polynomials. Using this operational matrix, the given problem is converted into a set of algebraic equations. Illustrative examples are are given to demonstrate the efficiency and simplicity of this technique.

Stable multi-domain spectral penalty methods for fractional partial differential equations

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Xu, Qinwu; Hesthaven, Jan S.

2014-01-01

We propose stable multi-domain spectral penalty methods suitable for solving fractional partial differential equations with fractional derivatives of any order. First, a high order discretization is proposed to approximate fractional derivatives of any order on any given grids based on orthogonal polynomials. The approximation order is analyzed and verified through numerical examples. Based on the discrete fractional derivative, we introduce stable multi-domain spectral penalty methods for solving fractional advection and diffusion equations. The equations are discretized in each sub-domain separately and the global schemes are obtained by weakly imposed boundary and interface conditions through a penalty term. Stability of the schemes are analyzed and numerical examples based on both uniform and nonuniform grids are considered to highlight the flexibility and high accuracy of the proposed schemes.

Validation of a motion-robust 2D sequential technique for quantification of hepatic proton density fat fraction during free breathing.

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Pooler, B Dustin; Hernando, Diego; Ruby, Jeannine A; Ishii, Hiroshi; Shimakawa, Ann; Reeder, Scott B

2018-04-17

Current chemical-shift-encoded (CSE) MRI techniques for measuring hepatic proton density fat fraction (PDFF) are sensitive to motion artifacts. Initial validation of a motion-robust 2D-sequential CSE-MRI technique for quantification of hepatic PDFF. Phantom study and prospective in vivo cohort. Fifty adult patients (27 women, 23 men, mean age 57.2 years). 3D, 2D-interleaved, and 2D-sequential CSE-MRI acquisitions at 1.5T. Three CSE-MRI techniques (3D, 2D-interleaved, 2D-sequential) were performed in a PDFF phantom and in vivo. Reference standards were 3D CSE-MRI PDFF measurements for the phantom study and single-voxel MR spectroscopy hepatic PDFF measurements (MRS-PDFF) in vivo. In vivo hepatic MRI-PDFF measurements were performed during a single breath-hold (BH) and free breathing (FB), and were repeated by a second reader for the FB 2D-sequential sequence to assess interreader variability. Correlation plots to validate the 2D-sequential CSE-MRI against the phantom and in vivo reference standards. Bland-Altman analysis of FB versus BH CSE-MRI acquisitions to evaluate robustness to motion. Bland-Altman analysis to assess interreader variability. Phantom 2D-sequential CSE-MRI PDFF measurements demonstrated excellent agreement and correlation (R 2 > 0.99) with 3D CSE-MRI. In vivo, the mean (±SD) hepatic PDFF was 8.8 ± 8.7% (range 0.6-28.5%). Compared with BH acquisitions, FB hepatic PDFF measurements demonstrated bias of +0.15% for 2D-sequential compared with + 0.53% for 3D and +0.94% for 2D-interleaved. 95% limits of agreement (LOA) were narrower for 2D-sequential (±0.99%), compared with 3D (±3.72%) and 2D-interleaved (±3.10%). All CSE-MRI techniques had excellent correlation with MRS (R 2 > 0.97). The FB 2D-sequential acquisition demonstrated little interreader variability, with mean bias of +0.07% and 95% LOA of ± 1.53%. This motion-robust 2D-sequential CSE-MRI can accurately measure hepatic PDFF during free breathing in a patient population with

Design of fractional order differentiator using type-III and type-IV discrete cosine transform

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Manjeet Kumar

2017-02-01

Full Text Available In this paper, an interpolation method based on discrete cosine transform (DCT is employed for digital finite impulse response-fractional order differentiator (FIR-FOD design. Here, a fractional order digital differentiator is modeled as finite impulse response (FIR system to get an optimized frequency response that approximates the ideal response of a fractional order differentiator. Next, DCT-III and DCT-IV are utilized to determine the filter coefficients of FIR filter that compute the Fractional derivative of a given signal. To improve the frequency response of the proposed FIR-FOD, the filter coefficients are further modified using windows. Several design examples are presented to demonstrate the superiority of the proposed method. The simulation results have also been compared with the existing FIR-FOD design methods such as DFT interpolation, radial basis function (RBF interpolation, DCT-II interpolation and DST interpolation methods. The result reveals that the proposed FIR-FOD design technique using DCT-III and DCT-IV outperforms DFT interpolation, RBF interpolation, DCT-II interpolation and DST interpolation methods in terms of magnitude error.

The influence of fractionation on cell survival and premature differentiation after carbon ion irradiation

International Nuclear Information System (INIS)

Wang Jufang; Li Renming; Guo Chuanling; Fournier, C.; K-Weyrather, W.

2008-01-01

To investigate the influence of fractionation on cell survival and radiation induced premature differentiation as markers for early and late effects after X-rays and carbon irradiation. Normal human fibroblasts NHDF, AG1522B and WI-38 were irradiated with 250 kV X-rays, or 266 MeV/u, 195 MeV/u and 11 MeV/u carbon ions. Cytotoxicity was measured by a clonogenic survival assay or by determination of the differentiation pattern. Experiments with high-energy carbon ions show that fractionation induced repair effects are similar to photon irradiation. The relative biological effective (RBE) 10 values for clonogenic survival are 1.3 and 1.6 for irradiation in one or two fractions for NHDF cells and around 1.2 for AG1522B cells regardless of the fractionation scheme. The RBE for a doubling of post mitotic fibroblasts (PMF) in the population is 1 for both single and two fractionated irradiation of NHDF cells. Using 11 MeV/u carbon ions, no repair effect can be seen in WI-38 cells. The RBE 10 for clonogenic survival is 3.2 for single irradiation and 4.9 for two fractionated irradiations. The RBE for a doubling of PMF is 3.1 and 5.0 for single and two fractionated irradiations, respectively. For both cell lines the effects of high-energy carbon ions representing the irradiation of the skin and the normal tissue in the entrance channel are similar to the effects of X-rays. The fractionation effects are maintained. For the lower energy, which is representative for the irradiation of the tumor region, RBE is enhanced for clonogenic survival as well as for premature terminal differentiation. Fractionation effects are not detectable. Consequently, the therapeutic ratio is significantly enhanced by fractionated irradiation with carbon ions. (author)

Existence of smooth solutions of multi-term Caputo-type fractional differential equations

OpenAIRE

Sin, Chung-Sik; Cheng, Shusen; Ri, Gang-Il; Kim, Mun-Chol

2017-01-01

This paper deals with the initial value problem for the multi-term fractional differential equation. The fractional derivative is defined in the Caputo sense. Firstly the initial value problem is transformed into a equivalent Volterra-type integral equation under appropriate assumptions. Then new existence results for smooth solutions are established by using the Schauder fixed point theorem.

A New Numerical Technique for Solving Systems Of Nonlinear Fractional Partial Differential Equations

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Mountassir Hamdi Cherif

2017-11-01

Full Text Available In this paper, we apply an efficient method called the Aboodh decomposition method to solve systems of nonlinear fractional partial differential equations. This method is a combined form of Aboodh transform with Adomian decomposition method. The theoretical analysis of this investigated for systems of nonlinear fractional partial differential equations is calculated in the explicit form of a power series with easily computable terms. Some examples are given to shows that this method is very efficient and accurate. This method can be applied to solve others nonlinear systems problems.

The numerical solution of linear multi-term fractional differential equations: systems of equations

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Edwards, John T.; Ford, Neville J.; Simpson, A. Charles

2002-11-01

In this paper, we show how the numerical approximation of the solution of a linear multi-term fractional differential equation can be calculated by reduction of the problem to a system of ordinary and fractional differential equations each of order at most unity. We begin by showing how our method applies to a simple class of problems and we give a convergence result. We solve the Bagley Torvik equation as an example. We show how the method can be applied to a general linear multi-term equation and give two further examples.

TRAVELING WAVE SOLUTIONS OF SOME FRACTIONAL DIFFERENTIAL EQUATIONS

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SERIFE MUGE EGE

2016-07-01

Full Text Available The modified Kudryashov method is powerful, efficient and can be used as an alternative to establish new solutions of different type of fractional differential equations applied in mathematical physics. In this article, we’ve constructed new traveling wave solutions including symmetrical Fibonacci function solutions, hyperbolic function solutions and rational solutions of the space-time fractional Cahn Hillihard equation D_t^α u − γD_x^α u − 6u(D_x^α u^2 − (3u^2 − 1D_x^α (D_x^α u + D_x^α(D_x^α(D_x^α(D_x^α u = 0 and the space-time fractional symmetric regularized long wave (SRLW equation D_t^α(D_t^α u + D_x^α(D_x^α u + uD_t^α(D_x^α u + D_x^α u D_t^α u + D_t^α(D_t^α(D_x^α(D_x^α u = 0 via modified Kudryashov method. In addition, some of the solutions are described in the figures with the help of Mathematica.

On Analytical Solutions of the Fractional Differential Equation with Uncertainty: Application to the Basset Problem

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Soheil Salahshour

2015-02-01

Full Text Available In this paper, we apply the concept of Caputo’s H-differentiability, constructed based on the generalized Hukuhara difference, to solve the fuzzy fractional differential equation (FFDE with uncertainty. This is in contrast to conventional solutions that either require a quantity of fractional derivatives of unknown solution at the initial point (Riemann–Liouville or a solution with increasing length of their support (Hukuhara difference. Then, in order to solve the FFDE analytically, we introduce the fuzzy Laplace transform of the Caputo H-derivative. To the best of our knowledge, there is limited research devoted to the analytical methods to solve the FFDE under the fuzzy Caputo fractional differentiability. An analytical solution is presented to confirm the capability of the proposed method.

Numerical Solution of Stochastic Nonlinear Fractional Differential Equations

KAUST Repository

El-Beltagy, Mohamed A.

2015-01-07

Using Wiener-Hermite expansion (WHE) technique in the solution of the stochastic partial differential equations (SPDEs) has the advantage of converting the problem to a system of deterministic equations that can be solved efficiently using the standard deterministic numerical methods [1]. WHE is the only known expansion that handles the white/colored noise exactly. This work introduces a numerical estimation of the stochastic response of the Duffing oscillator with fractional or variable order damping and driven by white noise. The WHE technique is integrated with the Grunwald-Letnikov approximation in case of fractional order and with Coimbra approximation in case of variable-order damping. The numerical solver was tested with the analytic solution and with Monte-Carlo simulations. The developed mixed technique was shown to be efficient in simulating SPDEs.

Numerical Solution of Stochastic Nonlinear Fractional Differential Equations

KAUST Repository

El-Beltagy, Mohamed A.; Al-Juhani, Amnah

2015-01-01

Using Wiener-Hermite expansion (WHE) technique in the solution of the stochastic partial differential equations (SPDEs) has the advantage of converting the problem to a system of deterministic equations that can be solved efficiently using the standard deterministic numerical methods [1]. WHE is the only known expansion that handles the white/colored noise exactly. This work introduces a numerical estimation of the stochastic response of the Duffing oscillator with fractional or variable order damping and driven by white noise. The WHE technique is integrated with the Grunwald-Letnikov approximation in case of fractional order and with Coimbra approximation in case of variable-order damping. The numerical solver was tested with the analytic solution and with Monte-Carlo simulations. The developed mixed technique was shown to be efficient in simulating SPDEs.

Particular Solutions of the Confluent Hypergeometric Differential Equation by Using the Nabla Fractional Calculus Operator

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Resat Yilmazer

2016-02-01

Full Text Available In this work; we present a method for solving the second-order linear ordinary differential equation of hypergeometric type. The solutions of this equation are given by the confluent hypergeometric functions (CHFs. Unlike previous studies, we obtain some different new solutions of the equation without using the CHFs. Therefore, we obtain new discrete fractional solutions of the homogeneous and non-homogeneous confluent hypergeometric differential equation (CHE by using a discrete fractional Nabla calculus operator. Thus, we obtain four different new discrete complex fractional solutions for these equations.

Numerical Solution of the Fractional Partial Differential Equations by the Two-Dimensional Fractional-Order Legendre Functions

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Fukang Yin

2013-01-01

Full Text Available A numerical method is presented to obtain the approximate solutions of the fractional partial differential equations (FPDEs. The basic idea of this method is to achieve the approximate solutions in a generalized expansion form of two-dimensional fractional-order Legendre functions (2D-FLFs. The operational matrices of integration and derivative for 2D-FLFs are first derived. Then, by these matrices, a system of algebraic equations is obtained from FPDEs. Hence, by solving this system, the unknown 2D-FLFs coefficients can be computed. Three examples are discussed to demonstrate the validity and applicability of the proposed method.

Analytical Solutions of Fractional Differential Equations Using the Convenient Adomian Series

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Xiang-Chao Shi

2014-01-01

Full Text Available Due to the memory trait of the fractional calculus, numerical or analytical solution of higher order becomes very difficult even impossible to obtain in real engineering problems. Recently, a new and convenient way was suggested to calculate the Adomian series and the higher order approximation was realized. In this paper, the Adomian decomposition method is applied to nonlinear fractional differential equation and the error analysis is given which shows the convenience.

Single-Fraction Stereotactic Body Radiation Therapy and Sequential Gemcitabine for the Treatment of Locally Advanced Pancreatic Cancer

International Nuclear Information System (INIS)

Schellenberg, Devin; Kim, Jeff; Christman-Skieller, Claudia; Chun, Carlene L.; Columbo, Laurie Ann; Ford, James M.; Fisher, George A.; Kunz, Pamela L.; Van Dam, Jacques; Quon, Andrew; Desser, Terry S.; Norton, Jeffrey; Hsu, Annie; Maxim, Peter G.; Xing, Lei; Goodman, Karyn A.; Chang, Daniel T.; Koong, Albert C.

2011-01-01

Purpose: This Phase II trial evaluated the toxicity, local control, and overall survival in patients treated with sequential gemcitabine and linear accelerator-based single-fraction stereotactic body radiotherapy (SBRT). Methods and Materials: Twenty patients with locally advanced, nonmetastatic pancreatic adenocarcinoma were enrolled on this prospective single-institution, institutional review board-approved study. Gemcitabine was administered on Days 1, 8, and 15, and SBRT on Day 29. Gemcitabine was restarted on Day 43 and continued for 3-5 cycles. SBRT of 25 Gy in a single fraction was delivered to the internal target volume with a 2- 3-mm margin using a nine-field intensity-modulated radiotherapy technique. Respiratory gating was used to account for breathing motion. Follow-up evaluations occurred at 4-6 weeks, 10-12 weeks, and every 3 months after SBRT. Results: All patients completed SBRT and a median of five cycles of chemotherapy. Follow-up for the 2 remaining alive patients was 25.1 and 36.4 months. No acute Grade 3 or greater nonhematologic toxicity was observed. Late Grade 3 or greater toxicities occurred in 1 patient (5%) and consisted of a duodenal perforation (G4). Three patients (15%) developed ulcers (G2) that were medically managed. Overall, median survival was 11.8 months, with 1-year survival of 50% and 2-year survival of 20%. Using serial computed tomography, the freedom from local progression was 94% at 1 year. Conclusion: Linear accelerator-delivered SBRT with sequential gemcitabine resulted in excellent local control of locally advanced pancreatic cancer. Future studies will address strategies for reducing long-term duodenal toxicity associated with SBRT.

Abstract fractional integro-differential equations involving nonlocal initial conditions in α-norm

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Wang Rong-Nian

2011-01-01

Full Text Available Abstract In the present paper, we deal with the Cauchy problems of abstract fractional integro-differential equations involving nonlocal initial conditions in α-norm, where the operator A in the linear part is the generator of a compact analytic semigroup. New criterions, ensuring the existence of mild solutions, are established. The results are obtained by using the theory of operator families associated with the function of Wright type and the semigroup generated by A, Krasnoselkii's fixed point theorem and Schauder's fixed point theorem. An application to a fractional partial integro-differential equation with nonlocal initial condition is also considered. Mathematics subject classification (2000 26A33, 34G10, 34G20

Sequential attack with intensity modulation on the differential-phase-shift quantum-key-distribution protocol

International Nuclear Information System (INIS)

Tsurumaru, Toyohiro

2007-01-01

In this paper, we discuss the security of the differential-phase-shift quantum-key-distribution (DPSQKD) protocol by introducing an improved version of the so-called sequential attack, which was originally discussed by Waks et al. [Phys. Rev. A 73, 012344 (2006)]. Our attack differs from the original form of the sequential attack in that the attacker Eve modulates not only the phases but also the amplitude in the superposition of the single-photon states which she sends to the receiver. Concentrating especially on the 'discretized Gaussian' intensity modulation, we show that our attack is more effective than the individual attack, which had been the best attack up to present. As a result of this, the recent experiment with communication distance of 100 km reported by Diamanti et al. [Opt. Express 14, 13073 (2006)] turns out to be insecure. Moreover, it can be shown that in a practical experimental setup which is commonly used today, the communication distance achievable by the DPSQKD protocol is less than 95 km

Ulam stability for fractional differential equations in the sense of Caputo operator

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Rabha W. Ibrahim

2012-12-01

Full Text Available In this paper, we consider the Hyers-Ulam stability for the following fractional differential equations, in the sense ofcomplex Caputo fractional derivative defined, in the unit disk: cDßzf(z=G(f(z, cDázf(z,zf‘(z;z 0<á<1<ß<2 . Furthermore,a generalization of the admissible functions in complex Banach spaces is imposed and applications are illustrated.

On conservation laws for models in discrete, noncommutative and fractional differential calculus

International Nuclear Information System (INIS)

Klimek, M.

2001-01-01

We present the general method of derivation the explicit form of conserved currents for equations built within the framework of discrete, noncommutative or fractional differential calculus. The procedure applies to linear models with variable coefficients including also nonlinear potential part. As an example an equation on quantum plane, nonlinear Toda lattice model and homogeneous equation of fractional diffusion in 1+1 dimensions are studied

Robust fast controller design via nonlinear fractional differential equations.

Science.gov (United States)

Zhou, Xi; Wei, Yiheng; Liang, Shu; Wang, Yong

2017-07-01

A new method for linear system controller design is proposed whereby the closed-loop system achieves both robustness and fast response. The robustness performance considered here means the damping ratio of closed-loop system can keep its desired value under system parameter perturbation, while the fast response, represented by rise time of system output, can be improved by tuning the controller parameter. We exploit techniques from both the nonlinear systems control and the fractional order systems control to derive a novel nonlinear fractional order controller. For theoretical analysis of the closed-loop system performance, two comparison theorems are developed for a class of fractional differential equations. Moreover, the rise time of the closed-loop system can be estimated, which facilitates our controller design to satisfy the fast response performance and maintain the robustness. Finally, numerical examples are given to illustrate the effectiveness of our methods. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Parareal algorithms with local time-integrators for time fractional differential equations

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Wu, Shu-Lin; Zhou, Tao

2018-04-01

It is challenge work to design parareal algorithms for time-fractional differential equations due to the historical effect of the fractional operator. A direct extension of the classical parareal method to such equations will lead to unbalance computational time in each process. In this work, we present an efficient parareal iteration scheme to overcome this issue, by adopting two recently developed local time-integrators for time fractional operators. In both approaches, one introduces auxiliary variables to localized the fractional operator. To this end, we propose a new strategy to perform the coarse grid correction so that the auxiliary variables and the solution variable are corrected separately in a mixed pattern. It is shown that the proposed parareal algorithm admits robust rate of convergence. Numerical examples are presented to support our conclusions.

Constructing and predicting solitary pattern solutions for nonlinear time-fractional dispersive partial differential equations

Science.gov (United States)

Arqub, Omar Abu; El-Ajou, Ahmad; Momani, Shaher

2015-07-01

Building fractional mathematical models for specific phenomena and developing numerical or analytical solutions for these fractional mathematical models are crucial issues in mathematics, physics, and engineering. In this work, a new analytical technique for constructing and predicting solitary pattern solutions of time-fractional dispersive partial differential equations is proposed based on the generalized Taylor series formula and residual error function. The new approach provides solutions in the form of a rapidly convergent series with easily computable components using symbolic computation software. For method evaluation and validation, the proposed technique was applied to three different models and compared with some of the well-known methods. The resultant simulations clearly demonstrate the superiority and potentiality of the proposed technique in terms of the quality performance and accuracy of substructure preservation in the construct, as well as the prediction of solitary pattern solutions for time-fractional dispersive partial differential equations.

Analytical approaches for the approximate solution of a nonlinear fractional ordinary differential equation

International Nuclear Information System (INIS)

Basak, K C; Ray, P C; Bera, R K

2009-01-01

The aim of the present analysis is to apply the Adomian decomposition method and He's variational method for the approximate analytical solution of a nonlinear ordinary fractional differential equation. The solutions obtained by the above two methods have been numerically evaluated and presented in the form of tables and also compared with the exact solution. It was found that the results obtained by the above two methods are in excellent agreement with the exact solution. Finally, a surface plot of the approximate solutions of the fractional differential equation by the above two methods is drawn for 0≤t≤2 and 1<α≤2.

From stochastic processes to numerical methods: A new scheme for solving reaction subdiffusion fractional partial differential equations

Energy Technology Data Exchange (ETDEWEB)

Angstmann, C.N.; Donnelly, I.C. [School of Mathematics and Statistics, UNSW Australia, Sydney NSW 2052 (Australia); Henry, B.I., E-mail: B.Henry@unsw.edu.au [School of Mathematics and Statistics, UNSW Australia, Sydney NSW 2052 (Australia); Jacobs, B.A. [School of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg, Private Bag 3, Wits 2050 (South Africa); DST–NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS) (South Africa); Langlands, T.A.M. [Department of Mathematics and Computing, University of Southern Queensland, Toowoomba QLD 4350 (Australia); Nichols, J.A. [School of Mathematics and Statistics, UNSW Australia, Sydney NSW 2052 (Australia)

2016-02-15

We have introduced a new explicit numerical method, based on a discrete stochastic process, for solving a class of fractional partial differential equations that model reaction subdiffusion. The scheme is derived from the master equations for the evolution of the probability density of a sum of discrete time random walks. We show that the diffusion limit of the master equations recovers the fractional partial differential equation of interest. This limiting procedure guarantees the consistency of the numerical scheme. The positivity of the solution and stability results are simply obtained, provided that the underlying process is well posed. We also show that the method can be applied to standard reaction–diffusion equations. This work highlights the broader applicability of using discrete stochastic processes to provide numerical schemes for partial differential equations, including fractional partial differential equations.

Multiple Positive Solutions for Nonlinear Semipositone Fractional Differential Equations

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Wen-Xue Zhou

2012-01-01

Full Text Available We present some new multiplicity of positive solutions results for nonlinear semipositone fractional boundary value problem D0+αu(t=p(tf(t,u(t-q(t,0differentiation. One example is also given to illustrate the main result.

Fractional Sobolev’s Spaces on Time Scales via Conformable Fractional Calculus and Their Application to a Fractional Differential Equation on Time Scales

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Yanning Wang

2016-01-01

Full Text Available Using conformable fractional calculus on time scales, we first introduce fractional Sobolev spaces on time scales, characterize them, and define weak conformable fractional derivatives. Second, we prove the equivalence of some norms in the introduced spaces and derive their completeness, reflexivity, uniform convexity, and compactness of some imbeddings, which can be regarded as a novelty item. Then, as an application, we present a recent approach via variational methods and critical point theory to obtain the existence of solutions for a p-Laplacian conformable fractional differential equation boundary value problem on time scale T:  Tα(Tαup-2Tα(u(t=∇F(σ(t,u(σ(t, Δ-a.e.  t∈a,bTκ2, u(a-u(b=0, Tα(u(a-Tα(u(b=0, where Tα(u(t denotes the conformable fractional derivative of u of order α at t, σ is the forward jump operator, a,b∈T,  01, and F:[0,T]T×RN→R. By establishing a proper variational setting, we obtain three existence results. Finally, we present two examples to illustrate the feasibility and effectiveness of the existence results.

Existence of Positive Solutions to a Boundary Value Problem for a Delayed Nonlinear Fractional Differential System

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Chen Yuming

2011-01-01

Full Text Available Though boundary value problems for fractional differential equations have been extensively studied, most of the studies focus on scalar equations and the fractional order between 1 and 2. On the other hand, delay is natural in practical systems. However, not much has been done for fractional differential equations with delays. Therefore, in this paper, we consider a boundary value problem of a general delayed nonlinear fractional system. With the help of some fixed point theorems and the properties of the Green function, we establish several sets of sufficient conditions on the existence of positive solutions. The obtained results extend and include some existing ones and are illustrated with some examples for their feasibility.

Fractional vector calculus and fractional Maxwell's equations

International Nuclear Information System (INIS)

Tarasov, Vasily E.

2008-01-01

The theory of derivatives and integrals of non-integer order goes back to Leibniz, Liouville, Grunwald, Letnikov and Riemann. The history of fractional vector calculus (FVC) has only 10 years. The main approaches to formulate a FVC, which are used in the physics during the past few years, will be briefly described in this paper. We solve some problems of consistent formulations of FVC by using a fractional generalization of the Fundamental Theorem of Calculus. We define the differential and integral vector operations. The fractional Green's, Stokes' and Gauss's theorems are formulated. The proofs of these theorems are realized for simplest regions. A fractional generalization of exterior differential calculus of differential forms is discussed. Fractional nonlocal Maxwell's equations and the corresponding fractional wave equations are considered

Sequential Isolation of Saturated, Aromatic, Resinic and Asphaltic Fractions Degrading Bacteria from Oil Contaminated Soil in South Sumatera

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Pingkan Aditiawati

2012-04-01

Full Text Available Sequential isolation has been conducted to obtain isolates of saturated, aromatic, resin, and asphaltene fractions degrading bacteria from oil contaminated sites. Five soil samples were collected from South Sumatera. These were analyzed using soil extract medium enriched with oil recovery or Remaining-Oil recovery Degradated (ROD as sole carbon and energy sources according to the isolation stage. ROD at the end of every isolation stage analyzed oil fractions by use of the SARA analysis method. Six isolates of bacteria have been selected, one isolate was fraction saturates degrading bacteria that are Mycobacterium sp. T1H2D4-7 at degradation rate 0.0199 mgs/h with density 8.4x106 cfu/g from stage I. The isolate T2H1D2-4, identified as Pseudomonas sp. was fraction aromatics degrading bacteria at accelerate 0.0141 mgs/h with density 5.1x106 cfu/g are obtained at stage II. Two isolates namely Micrococcus sp. T3H2D4-2 and Pseudomonas sp. T1H1D5-5 were fraction resins degrading bacteria by accelerate 0.0088 mgs/h at density 5.6x106 cfu/g and 0.0089 mgs/h at density 5.7x106 cfu/g are obtained at stage III. Isolation of stage IV has been obtained two isolates Pseudomonas sp. T4H1D3-1and Pseudomonas sp. T4H3D5-4 were fraction asphaltenes degrading bacteria by accelerate 0.0057 mgs/h at density 5.6x106 cfu/g and accelerate 0.0058 mgs/h at density 5.7x106 cfu/g.

High-order fractional partial differential equation transform for molecular surface construction.

Science.gov (United States)

Hu, Langhua; Chen, Duan; Wei, Guo-Wei

2013-01-01

Fractional derivative or fractional calculus plays a significant role in theoretical modeling of scientific and engineering problems. However, only relatively low order fractional derivatives are used at present. In general, it is not obvious what role a high fractional derivative can play and how to make use of arbitrarily high-order fractional derivatives. This work introduces arbitrarily high-order fractional partial differential equations (PDEs) to describe fractional hyperdiffusions. The fractional PDEs are constructed via fractional variational principle. A fast fractional Fourier transform (FFFT) is proposed to numerically integrate the high-order fractional PDEs so as to avoid stringent stability constraints in solving high-order evolution PDEs. The proposed high-order fractional PDEs are applied to the surface generation of proteins. We first validate the proposed method with a variety of test examples in two and three-dimensional settings. The impact of high-order fractional derivatives to surface analysis is examined. We also construct fractional PDE transform based on arbitrarily high-order fractional PDEs. We demonstrate that the use of arbitrarily high-order derivatives gives rise to time-frequency localization, the control of the spectral distribution, and the regulation of the spatial resolution in the fractional PDE transform. Consequently, the fractional PDE transform enables the mode decomposition of images, signals, and surfaces. The effect of the propagation time on the quality of resulting molecular surfaces is also studied. Computational efficiency of the present surface generation method is compared with the MSMS approach in Cartesian representation. We further validate the present method by examining some benchmark indicators of macromolecular surfaces, i.e., surface area, surface enclosed volume, surface electrostatic potential and solvation free energy. Extensive numerical experiments and comparison with an established surface model

Approximate controllability of Sobolev type fractional stochastic nonlocal nonlinear differential equations in Hilbert spaces

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Mourad Kerboua

2014-12-01

Full Text Available We introduce a new notion called fractional stochastic nonlocal condition, and then we study approximate controllability of class of fractional stochastic nonlinear differential equations of Sobolev type in Hilbert spaces. We use Hölder's inequality, fixed point technique, fractional calculus, stochastic analysis and methods adopted directly from deterministic control problems for the main results. A new set of sufficient conditions is formulated and proved for the fractional stochastic control system to be approximately controllable. An example is given to illustrate the abstract results.

Positive Solutions for Coupled Nonlinear Fractional Differential Equations

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Wenning Liu

2014-01-01

Full Text Available We consider the existence of positive solutions for a coupled system of nonlinear fractional differential equations with integral boundary values. Assume the nonlinear term is superlinear in one equation and sublinear in the other equation. By constructing two cones K1, K2 and computing the fixed point index in product cone K1×K2, we obtain that the system has a pair of positive solutions. It is remarkable that it is established on the Cartesian product of two cones, in which the feature of two equations can be opposite.

The Analytical Solution of Some Fractional Ordinary Differential Equations by the Sumudu Transform Method

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Hasan Bulut

2013-01-01

Full Text Available We introduce the rudiments of fractional calculus and the consequent applications of the Sumudu transform on fractional derivatives. Once this connection is firmly established in the general setting, we turn to the application of the Sumudu transform method (STM to some interesting nonhomogeneous fractional ordinary differential equations (FODEs. Finally, we use the solutions to form two-dimensional (2D graphs, by using the symbolic algebra package Mathematica Program 7.

Fractional order differentiation and robust control design crone, h-infinity and motion control

CERN Document Server

Sabatier, Jocelyn; Melchior, Pierre; Oustaloup, Alain

2015-01-01

This monograph collates the past decade’s work on fractional models and fractional systems in the fields of analysis, robust control and path tracking. Themes such as PID control, robust path tracking design and motion control methodologies involving fractional differentiation are amongst those explored. It juxtaposes recent theoretical results at the forefront in the field, and applications that can be used as exercises that will help the reader to assimilate the proposed methodologies. The first part of the book deals with fractional derivative and fractional model definitions, as well as recent results for stability analysis, fractional model physical interpretation, controllability, and H-infinity norm computation. It also presents a critical point of view on model pseudo-state and “real state”, tackling the problem of fractional model initialization. Readers will find coverage of PID, Fractional PID and robust control in the second part of the book, which rounds off with an extension of H-infinity ...

Existence and discrete approximation for optimization problems governed by fractional differential equations

Science.gov (United States)

Bai, Yunru; Baleanu, Dumitru; Wu, Guo-Cheng

2018-06-01

We investigate a class of generalized differential optimization problems driven by the Caputo derivative. Existence of weak Carathe ´odory solution is proved by using Weierstrass existence theorem, fixed point theorem and Filippov implicit function lemma etc. Then a numerical approximation algorithm is introduced, and a convergence theorem is established. Finally, a nonlinear programming problem constrained by the fractional differential equation is illustrated and the results verify the validity of the algorithm.

Measurement of the differential branching fraction of the decay $\\Lambda_b^0 \\rightarrow \\Lambda\\mu^+\\mu^-$

CERN Document Server

Aaij, R; Adinolfi, M; Adrover, C; Affolder, A; Ajaltouni, Z; Albrecht, J; Alessio, F; Alexander, M; Ali, S; Alkhazov, G; Alvarez Cartelle, P; Alves Jr, A A; Amato, S; Amerio, S; Amhis, Y; Anderlini, L; Anderson, J; Andreassen, R; Andrews, J E; Appleby, R B; Aquines Gutierrez, O; Archilli, F; Artamonov, A; Artuso, M; Aslanides, E; Auriemma, G; Baalouch, M; Bachmann, S; Back, J J; Baesso, C; Balagura, V; Baldini, W; Barlow, R J; Barschel, C; Barsuk, S; Barter, W; Bauer, Th; Bay, A; Beddow, J; Bedeschi, F; Bediaga, I; Belogurov, S; Belous, K; Belyaev, I; Ben-Haim, E; Bencivenni, G; Benson, S; Benton, J; Berezhnoy, A; Bernet, R; Bettler, M -O; van Beuzekom, M; Bien, A; Bifani, S; Bird, T; Bizzeti, A; Bjørnstad, P M; Blake, T; Blanc, F; Blouw, J; Blusk, S; Bocci, V; Bondar, A; Bondar, N; Bonivento, W; Borghi, S; Borgia, A; Bowcock, T J V; Bowen, E; Bozzi, C; Brambach, T; van den Brand, J; Bressieux, J; Brett, D; Britsch, M; Britton, T; Brook, N H; Brown, H; Burducea, I; Bursche, A; Busetto, G; Buytaert, J; Cadeddu, S; Callot, O; Calvi, M; Calvo Gomez, M; Camboni, A; Campana, P; Campora Perez, D; Carbone, A; Carboni, G; Cardinale, R; Cardini, A; Carranza-Mejia, H; Carson, L; Carvalho Akiba, K; Casse, G; Castillo Garcia, L; Cattaneo, M; Cauet, Ch; Cenci, R; Charles, M; Charpentier, Ph; Chen, P; Chiapolini, N; Chrzaszcz, M; Ciba, K; Cid Vidal, X; Ciezarek, G; Clarke, P E L; Clemencic, M; Cliff, H V; Closier, J; Coca, C; Coco, V; Cogan, J; Cogneras, E; Collins, P; Comerma-Montells, A; Contu, A; Cook, A; Coombes, M; Coquereau, S; Corti, G; Couturier, B; Cowan, G A; Craik, D C; Cunliffe, S; Currie, R; D'Ambrosio, C; David, P; David, P N Y; Davis, A; De Bonis, I; De Bruyn, K; De Capua, S; De Cian, M; De Miranda, J M; De Paula, L; De Silva, W; De Simone, P; Decamp, D; Deckenhoff, M; Del Buono, L; Déléage, N; Derkach, D; Deschamps, O; Dettori, F; Di Canto, A; Di Ruscio, F; Dijkstra, H; Dogaru, M; Donleavy, S; Dordei, F; Dosil Suárez, A; Dossett, D; Dovbnya, A; Dupertuis, F; Durante, P; Dzhelyadin, R; Dziurda, A; Dzyuba, A; Easo, S; Egede, U; Egorychev, V; Eidelman, S; van Eijk, D; Eisenhardt, S; Eitschberger, U; Ekelhof, R; Eklund, L; El Rifai, I; Elsasser, Ch; Falabella, A; Färber, C; Fardell, G; Farinelli, C; Farry, S; Fave, V; Ferguson, D; Fernandez Albor, V; Ferreira Rodrigues, F; Ferro-Luzzi, M; Filippov, S; Fiore, M; Fitzpatrick, C; Fontana, M; Fontanelli, F; Forty, R; Francisco, O; Frank, M; Frei, C; Frosini, M; Furcas, S; Furfaro, E; Gallas Torreira, A; Galli, D; Gandelman, M; Gandini, P; Gao, Y; Garofoli, J; Garosi, P; Garra Tico, J; Garrido, L; Gaspar, C; Gauld, R; Gersabeck, E; Gersabeck, M; Gershon, T; Ghez, Ph; Gibson, V; Giubega, L; Gligorov, V V; Göbel, C; Golubkov, D; Golutvin, A; Gomes, A; Gordon, H; Grabalosa Gándara, M; Graciani Diaz, R; Granado Cardoso, L A; Graugés, E; Graziani, G; Grecu, A; Greening, E; Gregson, S; Griffith, P; Grünberg, O; Gui, B; Gushchin, E; Guz, Yu; Gys, T; Hadjivasiliou, C; Haefeli, G; Haen, C; Haines, S C; Hall, S; Hamilton, B; Hampson, T; Hansmann-Menzemer, S; Harnew, N; Harnew, S T; Harrison, J; Hartmann, T; He, J; Head, T; Heijne, V; Hennessy, K; Henrard, P; Hernando Morata, J A; van Herwijnen, E; Hicheur, A; Hicks, E; Hill, D; Hoballah, M; Holtrop, M; Hombach, C; Hopchev, P; Hulsbergen, W; Hunt, P; Huse, T; Hussain, N; Hutchcroft, D; Hynds, D; Iakovenko, V; Idzik, M; Ilten, P; Jacobsson, R; Jaeger, A; Jans, E; Jaton, P; Jawahery, A; Jing, F; John, M; Johnson, D; Jones, C R; Joram, C; Jost, B; Kaballo, M; Kandybei, S; Kanso, W; Karacson, M; Karbach, T M; Kenyon, I R; Ketel, T; Keune, A; Khanji, B; Kochebina, O; Komarov, I; Koopman, R F; Koppenburg, P; Korolev, M; Kozlinskiy, A; Kravchuk, L; Kreplin, K; Kreps, M; Krocker, G; Krokovny, P; Kruse, F; Kucharczyk, M; Kudryavtsev, V; Kvaratskheliya, T; La Thi, V N; Lacarrere, D; Lafferty, G; Lai, A; Lambert, D; Lambert, R W; Lanciotti, E; Lanfranchi, G; Langenbruch, C; Latham, T; Lazzeroni, C; Le Gac, R; van Leerdam, J; Lees, J -P; Lefèvre, R; Leflat, A; Lefrançois, J; Leo, S; Leroy, O; Lesiak, T; Leverington, B; Li, Y; Li Gioi, L; Liles, M; Lindner, R; Linn, C; Liu, B; Liu, G; Lohn, S; Longstaff, I; Lopes, J H; Lopez-March, N; Lu, H; Lucchesi, D; Luisier, J; Luo, H; Machefert, F; Machikhiliyan, I V; Maciuc, F; Maev, O; Malde, S; Manca, G; Mancinelli, G; Maratas, J; Marconi, U; Marino, P; Märki, R; Marks, J; Martellotti, G; Martens, A; Martín Sánchez, A; Martinelli, M; Martinez Santos, D; Martins Tostes, D; Massafferri, A; Matev, R; Mathe, Z; Matteuzzi, C; Maurice, E; Mazurov, A; Mc Skelly, B; McCarthy, J; McNab, A; McNulty, R; Meadows, B; Meier, F; Meissner, M; Merk, M; Milanes, D A; Minard, M -N; Molina Rodriguez, J; Monteil, S; Moran, D; Morawski, P; Mordà, A; Morello, M J; Mountain, R; Mous, I; Muheim, F; Müller, K; Muresan, R; Muryn, B; Muster, B; Naik, P; Nakada, T; Nandakumar, R; Nasteva, I; Needham, M; Neubert, S; Neufeld, N; Nguyen, A D; Nguyen, T D; Nguyen-Mau, C; Nicol, M; Niess, V; Niet, R; Nikitin, N; Nikodem, T; Nomerotski, A; Novoselov, A; Oblakowska-Mucha, A; Obraztsov, V; Oggero, S; Ogilvy, S; Okhrimenko, O; Oldeman, R; Orlandea, M; Otalora Goicochea, J M; Owen, P; Oyanguren, A; Pal, B K; Palano, A; Palutan, M; Panman, J; Papanestis, A; Pappagallo, M; Parkes, C; Parkinson, C J; Passaleva, G; Patel, G D; Patel, M; Patrick, G N; Patrignani, C; Pavel-Nicorescu, C; Pazos Alvarez, A; Pellegrino, A; Penso, G; Pepe Altarelli, M; Perazzini, S; Perez Trigo, E; Pérez-Calero Yzquierdo, A; Perret, P; Perrin-Terrin, M; Pescatore, L; Pessina, G; Petridis, K; Petrolini, A; Phan, A; Picatoste Olloqui, E; Pietrzyk, B; Pilař, T; Pinci, D; Playfer, S; Plo Casasus, M; Polci, F; Polok, G; Poluektov, A; Polycarpo, E; Popov, A; Popov, D; Popovici, B; Potterat, C; Powell, A; Prisciandaro, J; Pritchard, A; Prouve, C; Pugatch, V; Puig Navarro, A; Punzi, G; Qian, W; Rademacker, J H; Rakotomiaramanana, B; Rangel, M S; Raniuk, I; Rauschmayr, N; Raven, G; Redford, S; Reid, M M; dos Reis, A C; Ricciardi, S; Richards, A; Rinnert, K; Rives Molina, V; 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Stoica, S; Stone, S; Storaci, B; Straticiuc, M; Straumann, U; Subbiah, V K; Sun, L; Swientek, S; Syropoulos, V; Szczekowski, M; Szczypka, P; Szumlak, T; T'Jampens, S; Teklishyn, M; Teodorescu, E; Teubert, F; Thomas, C; Thomas, E; van Tilburg, J; Tisserand, V; Tobin, M; Tolk, S; Tonelli, D; Topp-Joergensen, S; Torr, N; Tournefier, E; Tourneur, S; Tran, M T; Tresch, M; Tsaregorodtsev, A; Tsopelas, P; Tuning, N; Ubeda Garcia, M; Ukleja, A; Urner, D; Ustyuzhanin, A; Uwer, U; Vagnoni, V; Valenti, G; Vallier, A; Van Dijk, M; Vazquez Gomez, R; Vazquez Regueiro, P; Vázquez Sierra, C; Vecchi, S; Velthuis, J J; Veltri, M; Veneziano, G; Vesterinen, M; Viaud, B; Vieira, D; Vilasis-Cardona, X; Vollhardt, A; Volyanskyy, D; Voong, D; Vorobyev, A; Vorobyev, V; Voß, C; Voss, H; Waldi, R; Wallace, C; Wallace, R; Wandernoth, S; Wang, J; Ward, D R; Watson, N K; Webber, A D; Websdale, D; Whitehead, M; Wicht, J; Wiechczynski, J; Wiedner, D; Wiggers, L; Wilkinson, G; Williams, M P; Williams, M; Wilson, F F; Wimberley, J; Wishahi, J; Witek, M; Wotton, S A; Wright, S; Wu, S; Wyllie, K; Xie, Y; Xing, Z; Yang, Z; Young, R; Yuan, X; Yushchenko, O; Zangoli, M; Zavertyaev, M; Zhang, F; Zhang, L; Zhang, W C; Zhang, Y; Zhelezov, A; Zhokhov, A; Zhong, L; Zvyagin, A

2013-01-01

The differential branching fraction of the decay $\\Lambda_b^0\\rightarrow\\Lambda\\mu^+\\mu^-$ is measured as a function of the square of the dimuon invariant mass, $q^2$. A yield of $78\\pm12$ $\\Lambda_b^0\\rightarrow\\Lambda\\mu^+\\mu^-$ decays is observed using data, corresponding to an integrated luminosity of 1.0,fb$^{-1}$, collected by the LHCb experiment at a centre-of-mass energy of 7\\,TeV. A significant signal is found in the $q^2$ region above the square of the $J/\\psi$ mass, while at lower-$q^2$ values upper limits are set on the differential branching fraction. Integrating the differential branching fraction over $q^2$, while excluding the $J/\\psi$ and $\\psi(2S)$ regions, gives a branching fraction of $B(\\Lambda_b^0\\rightarrow\\Lambda\\mu^+\\mu^-)=(0.96\\pm 0.16(stat)\\pm 0.13(syst)\\pm 0.21 (\\mathrm{norm}))\\times 10^{-6}$, where the uncertainties are statistical, systematic and due to the normalisation mode, $\\Lambda_b^0\\rightarrow J/\\psi\\Lambda$, respectively.

Generalized Euler-Lagrange Equations for Fuzzy Fractional Variational Problems under gH-Atangana-Baleanu Differentiability

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Jianke Zhang

2018-01-01

Full Text Available We study in this paper the Atangana-Baleanu fractional derivative of fuzzy functions based on the generalized Hukuhara difference. Under the condition of gH-Atangana-Baleanu fractional differentiability, we prove the generalized necessary and sufficient optimality conditions for problems of the fuzzy fractional calculus of variations with a Lagrange function. The new kernel of gH-Atangana-Baleanu fractional derivative has no singularity and no locality, which was not precisely illustrated in the previous definitions.

Fractionation And Distribution Of Heavy Metals In street Dust In Amman, Jordan

International Nuclear Information System (INIS)

Jaradat, Q.

2002-01-01

Different types of street dust: major streets, minor streets, gas stations, traffic lights and car parks in Amman were subjected to size-fractionation into three sizes: 500-125μm , 125-53μm, and <53μm. Sequential extraction was also performed on the non-fractionated samples using Tessier procedure. The sequentially extracted and the fractionated samples were analyzed for Pb, Cd, Zn and Mn using flame atomic absorption. The silt fraction ( <53μm particles ) contains the highest concentrations of all elements in most types of street dust samples followed by the fine fraction ( 125-53μm particles). From the sequential extraction data, the highest concentrations of heavy metals were : Pb, Cd, Zn and in Fe-Mn oxide fraction, and Cu in the organic fraction. (author). 29 refs., 2 figs., 4 tabs

A NEW FRACTIONAL MODEL OF SINGLE DEGREE OF FREEDOM SYSTEM, BY USING GENERALIZED DIFFERENTIAL TRANSFORM METHOD

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HASHEM SABERI NAJAFI

2016-07-01

Full Text Available Generalized differential transform method (GDTM is a powerful method to solve the fractional differential equations. In this paper, a new fractional model for systems with single degree of freedom (SDOF is presented, by using the GDTM. The advantage of this method compared with some other numerical methods has been shown. The analysis of new approximations, damping and acceleration of systems are also described. Finally, by reducing damping and analysis of the errors, in one of the fractional cases, we have shown that in addition to having a suitable solution for the displacement close to the exact one, the system enjoys acceleration once crossing the equilibrium point.

Local fractional variational iteration algorithm iii for the diffusion model associated with non-differentiable heat transfer

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Meng Zhi-Jun

2016-01-01

Full Text Available This paper addresses a new application of the local fractional variational iteration algorithm III to solve the local fractional diffusion equation defined on Cantor sets associated with non-differentiable heat transfer.

Stability Analysis for Fractional-Order Linear Singular Delay Differential Systems

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Hai Zhang

2014-01-01

Full Text Available We investigate the delay-independently asymptotic stability of fractional-order linear singular delay differential systems. Based on the algebraic approach, the sufficient conditions are presented to ensure the asymptotic stability for any delay parameter. By applying the stability criteria, one can avoid solving the roots of transcendental equations. An example is also provided to illustrate the effectiveness and applicability of the theoretical results.

Scale-invariant solutions to partial differential equations of fractional order with a moving boundary condition

International Nuclear Information System (INIS)

Li Xicheng; Xu Mingyu; Wang Shaowei

2008-01-01

In this paper, we give similarity solutions of partial differential equations of fractional order with a moving boundary condition. The solutions are given in terms of a generalized Wright function. The time-fractional Caputo derivative and two types of space-fractional derivatives are considered. The scale-invariant variable and the form of the solution of the moving boundary are obtained by the Lie group analysis. A comparison between the solutions corresponding to two types of fractional derivative is also given

A higher order numerical method for time fractional partial differential equations with nonsmooth data

Science.gov (United States)

Xing, Yanyuan; Yan, Yubin

2018-03-01

Gao et al. [11] (2014) introduced a numerical scheme to approximate the Caputo fractional derivative with the convergence rate O (k 3 - α), 0 equation is sufficiently smooth, Lv and Xu [20] (2016) proved by using energy method that the corresponding numerical method for solving time fractional partial differential equation has the convergence rate O (k 3 - α), 0 equation has low regularity and in this case the numerical method fails to have the convergence rate O (k 3 - α), 0 quadratic interpolation polynomials. Based on this scheme, we introduce a time discretization scheme to approximate the time fractional partial differential equation and show by using Laplace transform methods that the time discretization scheme has the convergence rate O (k 3 - α), 0 0 for smooth and nonsmooth data in both homogeneous and inhomogeneous cases. Numerical examples are given to show that the theoretical results are consistent with the numerical results.

Cantor-type cylindrical-coordinate method for differential equations with local fractional derivatives

International Nuclear Information System (INIS)

Yang, Xiao-Jun; Srivastava, H.M.; He, Ji-Huan; Baleanu, Dumitru

2013-01-01

In this Letter, we propose to use the Cantor-type cylindrical-coordinate method in order to investigate a family of local fractional differential operators on Cantor sets. Some testing examples are given to illustrate the capability of the proposed method for the heat-conduction equation on a Cantor set and the damped wave equation in fractal strings. It is seen to be a powerful tool to convert differential equations on Cantor sets from Cantorian-coordinate systems to Cantor-type cylindrical-coordinate systems.

What do results of common sequential fractionation and single-step extractions tell us about P binding with Fe and Al compounds in non-calcareous sediments?

Czech Academy of Sciences Publication Activity Database

Jan, Jiří; Borovec, Jakub; Kopáček, Jiří; Hejzlar, Josef

2013-01-01

Roč. 47, č. 2 (2013), s. 547-557 ISSN 0043-1354 R&D Projects: GA ČR(CZ) GA206/09/1764; GA MZe(CZ) QH81012; GA MZe(CZ) QI102A265 Institutional support: RVO:60077344 Keywords : sequential fractionation * ascorbate and oxalate extration * non-calcareous sediments Subject RIV: DA - Hydrology ; Limnology Impact factor: 5.323, year: 2013

The non-differentiable solution for local fractional Laplace equation in steady heat-conduction problem

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Chen Jie-Dong

2016-01-01

Full Text Available In this paper, we investigate the local fractional Laplace equation in the steady heat-conduction problem. The solutions involving the non-differentiable graph are obtained by using the characteristic equation method (CEM via local fractional derivative. The obtained results are given to present the accuracy of the technology to solve the steady heat-conduction in fractal media.

Numerical Solution of Multiterm Fractional Differential Equations Using the Matrix Mittag–Leffler Functions

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Marina Popolizio

2018-01-01

Full Text Available Multiterm fractional differential equations (MTFDEs nowadays represent a widely used tool to model many important processes, particularly for multirate systems. Their numerical solution is then a compelling subject that deserves great attention, not least because of the difficulties to apply general purpose methods for fractional differential equations (FDEs to this case. In this paper, we first transform the MTFDEs into equivalent systems of FDEs, as done by Diethelm and Ford; in this way, the solution can be expressed in terms of Mittag–Leffler (ML functions evaluated at matrix arguments. We then propose to compute it by resorting to the matrix approach proposed by Garrappa and Popolizio. Several numerical tests are presented that clearly show that this matrix approach is very accurate and fast, also in comparison with other numerical methods.

Numerical approximations of nonlinear fractional differential difference equations by using modified He-Laplace method

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J. Prakash

2016-03-01

Full Text Available In this paper, a numerical algorithm based on a modified He-Laplace method (MHLM is proposed to solve space and time nonlinear fractional differential-difference equations (NFDDEs arising in physical phenomena such as wave phenomena in fluids, coupled nonlinear optical waveguides and nanotechnology fields. The modified He-Laplace method is a combined form of the fractional homotopy perturbation method and Laplace transforms method. The nonlinear terms can be easily decomposed by the use of He’s polynomials. This algorithm has been tested against time-fractional differential-difference equations such as the modified Lotka Volterra and discrete (modified KdV equations. The proposed scheme grants the solution in the form of a rapidly convergent series. Three examples have been employed to illustrate the preciseness and effectiveness of the proposed method. The achieved results expose that the MHLM is very accurate, efficient, simple and can be applied to other nonlinear FDDEs.

On a higher order multi-term time-fractional partial differential equation involving Caputo-Fabrizio derivative

OpenAIRE

Pirnapasov, Sardor; Karimov, Erkinjon

2017-01-01

In the present work we discuss higher order multi-term partial differential equation (PDE) with the Caputo-Fabrizio fractional derivative in time. We investigate a boundary value problem for fractional heat equation involving higher order Caputo-Fabrizio derivatives in time-variable. Using method of separation of variables and integration by parts, we reduce fractional order PDE to the integer order. We represent explicit solution of formulated problem in particular case by Fourier series.

Local fractional variational iteration algorithm II for non-homogeneous model associated with the non-differentiable heat flow

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Yu Zhang

2015-10-01

Full Text Available In this article, we begin with the non-homogeneous model for the non-differentiable heat flow, which is described using the local fractional vector calculus, from the first law of thermodynamics in fractal media point view. We employ the local fractional variational iteration algorithm II to solve the fractal heat equations. The obtained results show the non-differentiable behaviors of temperature fields of fractal heat flow defined on Cantor sets.

A Table Lookup Method for Exact Analytical Solutions of Nonlinear Fractional Partial Differential Equations

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Ji Juan-Juan

2017-01-01

Full Text Available A table lookup method for solving nonlinear fractional partial differential equations (fPDEs is proposed in this paper. Looking up the corresponding tables, we can quickly obtain the exact analytical solutions of fPDEs by using this method. To illustrate the validity of the method, we apply it to construct the exact analytical solutions of four nonlinear fPDEs, namely, the time fractional simplified MCH equation, the space-time fractional combined KdV-mKdV equation, the (2+1-dimensional time fractional Zoomeron equation, and the space-time fractional ZKBBM equation. As a result, many new types of exact analytical solutions are obtained including triangular periodic solution, hyperbolic function solution, singular solution, multiple solitary wave solution, and Jacobi elliptic function solution.

A finite difference method for space fractional differential equations with variable diffusivity coefficient

KAUST Repository

Mustapha, K.

2017-06-03

Anomalous diffusion is a phenomenon that cannot be modeled accurately by second-order diffusion equations, but is better described by fractional diffusion models. The nonlocal nature of the fractional diffusion operators makes substantially more difficult the mathematical analysis of these models and the establishment of suitable numerical schemes. This paper proposes and analyzes the first finite difference method for solving {\\\\em variable-coefficient} fractional differential equations, with two-sided fractional derivatives, in one-dimensional space. The proposed scheme combines first-order forward and backward Euler methods for approximating the left-sided fractional derivative when the right-sided fractional derivative is approximated by two consecutive applications of the first-order backward Euler method. Our finite difference scheme reduces to the standard second-order central difference scheme in the absence of fractional derivatives. The existence and uniqueness of the solution for the proposed scheme are proved, and truncation errors of order $h$ are demonstrated, where $h$ denotes the maximum space step size. The numerical tests illustrate the global $O(h)$ accuracy of our scheme, except for nonsmooth cases which, as expected, have deteriorated convergence rates.

A finite difference method for space fractional differential equations with variable diffusivity coefficient

KAUST Repository

Mustapha, K.; Furati, K.; Knio, Omar; Maitre, O. Le

2017-01-01

Anomalous diffusion is a phenomenon that cannot be modeled accurately by second-order diffusion equations, but is better described by fractional diffusion models. The nonlocal nature of the fractional diffusion operators makes substantially more difficult the mathematical analysis of these models and the establishment of suitable numerical schemes. This paper proposes and analyzes the first finite difference method for solving {\\em variable-coefficient} fractional differential equations, with two-sided fractional derivatives, in one-dimensional space. The proposed scheme combines first-order forward and backward Euler methods for approximating the left-sided fractional derivative when the right-sided fractional derivative is approximated by two consecutive applications of the first-order backward Euler method. Our finite difference scheme reduces to the standard second-order central difference scheme in the absence of fractional derivatives. The existence and uniqueness of the solution for the proposed scheme are proved, and truncation errors of order $h$ are demonstrated, where $h$ denotes the maximum space step size. The numerical tests illustrate the global $O(h)$ accuracy of our scheme, except for nonsmooth cases which, as expected, have deteriorated convergence rates.

Differential branching fraction and angular analysis of the decay $B_s^0 \\to \\phi \\mu^+\\mu^-$

CERN Document Server

Aaij, R; Adeva, B; Adinolfi, M; Adrover, C; Affolder, A; Ajaltouni, Z; Albrecht, J; Alessio, F; Alexander, M; Ali, S; Alkhazov, G; Alvarez Cartelle, P; Alves Jr, A A; Amato, S; Amerio, S; Amhis, Y; Anderlini, L; Anderson, J; Andreassen, R; Appleby, R B; Aquines Gutierrez, O; Archilli, F; Artamonov, A; Artuso, M; Aslanides, E; Auriemma, G; Bachmann, S; Back, J J; Baesso, C; Balagura, V; Baldini, W; Barlow, R J; Barschel, C; Barsuk, S; Barter, W; Bauer, Th; Bay, A; Beddow, J; Bedeschi, F; Bediaga, I; Belogurov, S; Belous, K; Belyaev, I; Ben-Haim, E; Bencivenni, G; Benson, S; Benton, J; Berezhnoy, A; Bernet, R; Bettler, M -O; van Beuzekom, M; Bien, A; Bifani, S; Bird, T; Bizzeti, A; Bjørnstad, P M; Blake, T; Blanc, F; Blouw, J; Blusk, S; Bocci, V; Bondar, A; Bondar, N; Bonivento, W; Borghi, S; Borgia, A; Bowcock, T J V; Bowen, E; Bozzi, C; Brambach, T; van den Brand, J; Bressieux, J; Brett, D; Britsch, M; Britton, T; Brook, N H; Brown, H; Burducea, I; Bursche, A; Busetto, G; Buytaert, J; Cadeddu, S; Callot, O; Calvi, M; Calvo Gomez, M; Camboni, A; Campana, P; Campora Perez, D; Carbone, A; Carboni, G; Cardinale, R; Cardini, A; Carranza-Mejia, H; Carson, L; Carvalho Akiba, K; Casse, G; Castillo Garcia, L; Cattaneo, M; Cauet, Ch; Charles, M; Charpentier, Ph; Chen, P; Chiapolini, N; Chrzaszcz, M; Ciba, K; Cid Vidal, X; Ciezarek, G; Clarke, P E L; Clemencic, M; Cliff, H V; Closier, J; Coca, C; Coco, V; Cogan, J; Cogneras, E; Collins, P; Comerma-Montells, A; Contu, A; Cook, A; Coombes, M; Coquereau, S; Corti, G; Couturier, B; Cowan, G A; Craik, D C; Cunliffe, S; Currie, R; D'Ambrosio, C; David, P; David, P N Y; Davis, A; De Bonis, I; De Bruyn, K; De Capua, S; De Cian, M; De Miranda, J M; De Paula, L; De Silva, W; De Simone, P; Decamp, D; Deckenhoff, M; Del Buono, L; Déléage, N; Derkach, D; Deschamps, O; Dettori, F; Di Canto, A; Di Ruscio, F; Dijkstra, H; Dogaru, M; Donleavy, S; Dordei, F; Dosil Suárez, A; Dossett, D; Dovbnya, A; Dupertuis, F; Dzhelyadin, R; Dziurda, A; Dzyuba, A; Easo, S; Egede, U; Egorychev, V; Eidelman, S; van Eijk, D; Eisenhardt, S; Eitschberger, U; Ekelhof, R; Eklund, L; El Rifai, I; Elsasser, Ch; Elsby, D; Falabella, A; Färber, C; Fardell, G; Farinelli, C; Farry, S; Fave, V; Ferguson, D; Fernandez Albor, V; Ferreira Rodrigues, F; Ferro-Luzzi, M; Filippov, S; Fiore, M; Fitzpatrick, C; Fontana, M; Fontanelli, F; Forty, R; Francisco, O; Frank, M; Frei, C; Frosini, M; Furcas, S; Furfaro, E; Gallas Torreira, A; Galli, D; Gandelman, M; Gandini, P; Gao, Y; Garofoli, J; Garosi, P; Garra Tico, J; Garrido, L; Gaspar, C; Gauld, R; Gersabeck, E; Gersabeck, M; Gershon, T; Ghez, Ph; Gibson, V; Gligorov, V V; Göbel, C; Golubkov, D; Golutvin, A; Gomes, A; Gordon, H; Grabalosa Gándara, M; Graciani Diaz, R; Granado Cardoso, L A; Graugés, E; Graziani, G; Grecu, A; Greening, E; Gregson, S; Griffith, P; Grünberg, O; Gui, B; Gushchin, E; Guz, Yu; Gys, T; Hadjivasiliou, C; Haefeli, G; Haen, C; Haines, S C; Hall, S; Hampson, T; Hansmann-Menzemer, S; Harnew, N; Harnew, S T; Harrison, J; Hartmann, T; He, J; Heijne, V; Hennessy, K; Henrard, P; Hernando Morata, J A; van Herwijnen, E; Hicheur, A; Hicks, E; Hill, D; Hoballah, M; Holtrop, M; Hombach, C; Hopchev, P; Hulsbergen, W; Hunt, P; Huse, T; Hussain, N; Hutchcroft, D; Hynds, D; Iakovenko, V; Idzik, M; Ilten, P; Jacobsson, R; Jaeger, A; Jans, E; Jaton, P; Jawahery, A; Jing, F; John, M; Johnson, D; Jones, C R; Joram, C; Jost, B; Kaballo, M; Kandybei, S; Karacson, M; Karbach, T M; Kenyon, I R; Kerzel, U; Ketel, T; Keune, A; Khanji, B; Kochebina, O; Komarov, I; Koopman, R F; Koppenburg, P; Korolev, M; Kozlinskiy, A; Kravchuk, L; Kreplin, K; Kreps, M; Krocker, G; Krokovny, P; Kruse, F; Kucharczyk, M; Kudryavtsev, V; Kvaratskheliya, T; La Thi, V N; Lacarrere, D; Lafferty, G; Lai, A; Lambert, D; Lambert, R W; Lanciotti, E; Lanfranchi, G; Langenbruch, C; Latham, T; Lazzeroni, C; Le Gac, R; van Leerdam, J; Lees, J -P; Lefèvre, R; Leflat, A; Lefrançois, J; Leo, S; Leroy, O; Lesiak, T; Leverington, B; Li, Y; Li Gioi, L; Liles, M; Lindner, R; Linn, C; Liu, B; Liu, G; Lohn, S; Longstaff, I; Lopes, J H; Lopez Asamar, E; Lopez-March, N; Lu, H; Lucchesi, D; Luisier, J; Luo, H; Machefert, F; Machikhiliyan, I V; Maciuc, F; Maev, O; Malde, S; Manca, G; Mancinelli, G; Marconi, U; Märki, R; Marks, J; Martellotti, G; Martens, A; Martin, L; Martín Sánchez, A; Martinelli, M; Martinez Santos, D; Martins Tostes, D; Massafferri, A; Matev, R; Mathe, Z; Matteuzzi, C; Maurice, E; Mazurov, A; Mc Skelly, B; McCarthy, J; McNab, A; McNulty, R; Meadows, B; Meier, F; Meissner, M; Merk, M; Milanes, D A; Minard, M -N; Molina Rodriguez, J; Monteil, S; Moran, D; Morawski, P; Morello, M J; Mountain, R; Mous, I; Muheim, F; Müller, K; Muresan, R; Muryn, B; Muster, B; Naik, P; Nakada, T; Nandakumar, R; Nasteva, I; Needham, M; Neufeld, N; Nguyen, A D; Nguyen, T D; Nguyen-Mau, C; Nicol, M; Niess, V; Niet, R; Nikitin, N; Nikodem, T; Nomerotski, A; Novoselov, A; Oblakowska-Mucha, A; Obraztsov, V; Oggero, S; Ogilvy, S; Okhrimenko, O; Oldeman, R; Orlandea, M; Otalora Goicochea, J M; Owen, P; Oyanguren, A; Pal, B K; Palano, A; Palutan, M; Panman, J; Papanestis, A; Pappagallo, M; Parkes, C; Parkinson, C J; Passaleva, G; Patel, G D; Patel, M; Patrick, G N; Patrignani, C; Pavel-Nicorescu, C; Pazos Alvarez, A; Pellegrino, A; Penso, G; Pepe Altarelli, M; Perazzini, S; Perego, D L; Perez Trigo, E; Pérez-Calero Yzquierdo, A; Perret, P; Perrin-Terrin, M; Pessina, G; Petridis, K; Petrolini, A; Phan, A; Picatoste Olloqui, E; Pietrzyk, B; Pilař, T; Pinci, D; Playfer, S; Plo Casasus, M; Polci, F; Polok, G; Poluektov, A; Polycarpo, E; Popov, A; Popov, D; Popovici, B; Potterat, C; Powell, A; Prisciandaro, J; Pritchard, A; Prouve, C; Pugatch, V; Puig Navarro, A; Punzi, G; Qian, W; Rademacker, J H; Rakotomiaramanana, B; Rangel, M S; Raniuk, I; Rauschmayr, N; Raven, G; Redford, S; Reid, M M; dos Reis, A C; Ricciardi, S; Richards, A; Rinnert, K; Rives Molina, V; Roa Romero, D A; Robbe, P; Rodrigues, E; Rodriguez Perez, P; Roiser, S; Romanovsky, V; Romero Vidal, A; Rouvinet, J; Ruf, T; Ruffini, F; Ruiz, H; Ruiz Valls, P; Sabatino, G; Saborido Silva, J J; Sagidova, N; Sail, P; Saitta, B; Salustino Guimaraes, V; Salzmann, C; Sanmartin Sedes, B; Sannino, M; Santacesaria, R; Santamarina Rios, C; Santovetti, E; Sapunov, M; Sarti, A; Satriano, C; Satta, A; Savrie, M; Savrina, D; Schaack, P; Schiller, M; Schindler, H; Schlupp, M; Schmelling, M; Schmidt, B; Schneider, O; Schopper, A; Schune, M -H; Schwemmer, R; Sciascia, B; Sciubba, A; Seco, M; Semennikov, A; Senderowska, K; Sepp, I; Serra, N; Serrano, J; Seyfert, P; Shapkin, M; Shapoval, I; Shatalov, P; Shcheglov, Y; Shears, T; Shekhtman, L; Shevchenko, O; Shevchenko, V; Shires, A; Silva Coutinho, R; Skwarnicki, T; Smith, N A; Smith, E; Smith, M; Sokoloff, M D; Soler, F J P; Soomro, F; Souza, D; Souza De Paula, B; Spaan, B; Sparkes, A; Spradlin, P; Stagni, F; Stahl, S; Steinkamp, O; Stoica, S; Stone, S; Storaci, B; Straticiuc, M; Straumann, U; Subbiah, V K; Sun, L; Swientek, S; Syropoulos, V; Szczekowski, M; Szczypka, P; Szumlak, T; T'Jampens, S; Teklishyn, M; Teodorescu, E; Teubert, F; Thomas, C; Thomas, E; van Tilburg, J; Tisserand, V; Tobin, M; Tolk, S; Tonelli, D; Topp-Joergensen, S; Torr, N; Tournefier, E; Tourneur, S; Tran, M T; Tresch, M; Tsaregorodtsev, A; Tsopelas, P; Tuning, N; Ubeda Garcia, M; Ukleja, A; Urner, D; Uwer, U; Vagnoni, V; Valenti, G; Vazquez Gomez, R; Vazquez Regueiro, P; Vecchi, S; Velthuis, J J; Veltri, M; Veneziano, G; Vesterinen, M; Viaud, B; Vieira, D; Vilasis-Cardona, X; Vollhardt, A; Volyanskyy, D; Voong, D; Vorobyev, A; Vorobyev, V; Voß, C; Voss, H; Waldi, R; Wallace, R; Wandernoth, S; Wang, J; Ward, D R; Watson, N K; Webber, A D; Websdale, D; Whitehead, M; Wicht, J; Wiechczynski, J; Wiedner, D; Wiggers, L; Wilkinson, G; Williams, M P; Williams, M; Wilson, F F; Wishahi, J; Witek, M; Wotton, S A; Wright, S; Wu, S; Wyllie, K; Xie, Y; Xing, F; Xing, Z; Yang, Z; Young, R; Yuan, X; Yushchenko, O; Zangoli, M; Zavertyaev, M; Zhang, F; Zhang, L; Zhang, W C; Zhang, Y; Zhelezov, A; Zhokhov, A; Zhong, L; Zvyagin, A

2013-07-11

The determination of the differential branching fraction and the first angular analysis of the decay $B_s^0\\to\\phi\\mu^{+}\\mu^{-}$ are presented using data, corresponding to an integrated luminosity of $1.0\\,{\\rm fb}^{-1}$, collected by the LHCb experiment at $\\sqrt{s}=7\\,{\\rm TeV}$. The differential branching fraction is determined in bins of $q^{2}$, the invariant dimuon mass squared. Integration over the full $q^{2}$ range yields a total branching fraction of ${\\cal B}(B_s^0\\to\\phi\\mu^{+}\\mu^{-}) = (7.07\\,^{+0.64}_{-0.59}\\pm 0.17 \\pm 0.71)\\times 10^{-7}$, where the first uncertainty is statistical, the second systematic, and the third originates from the branching fraction of the normalisation channel. An angular analysis is performed to determine the angular observables $F_{\\rm L}$, $S_3$, $A_6$, and $A_9$. The observables are consistent with Standard Model expectations.

Symbolic computation of analytic approximate solutions for nonlinear fractional differential equations

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Lin, Yezhi; Liu, Yinping; Li, Zhibin

2013-01-01

The Adomian decomposition method (ADM) is one of the most effective methods to construct analytic approximate solutions for nonlinear differential equations. In this paper, based on the new definition of the Adomian polynomials, Rach (2008) [22], the Adomian decomposition method and the Padé approximants technique, a new algorithm is proposed to construct analytic approximate solutions for nonlinear fractional differential equations with initial or boundary conditions. Furthermore, a MAPLE software package is developed to implement this new algorithm, which is user-friendly and efficient. One only needs to input the system equation, initial or boundary conditions and several necessary parameters, then our package will automatically deliver the analytic approximate solutions within a few seconds. Several different types of examples are given to illustrate the scope and demonstrate the validity of our package, especially for non-smooth initial value problems. Our package provides a helpful and easy-to-use tool in science and engineering simulations. Program summaryProgram title: ADMP Catalogue identifier: AENE_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENE_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 12011 No. of bytes in distributed program, including test data, etc.: 575551 Distribution format: tar.gz Programming language: MAPLE R15. Computer: PCs. Operating system: Windows XP/7. RAM: 2 Gbytes Classification: 4.3. Nature of problem: Constructing analytic approximate solutions of nonlinear fractional differential equations with initial or boundary conditions. Non-smooth initial value problems can be solved by this program. Solution method: Based on the new definition of the Adomian polynomials [1], the Adomian decomposition method and the Pad

Systems-based decomposition schemes for the approximate solution of multi-term fractional differential equations

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Ford, Neville J.; Connolly, Joseph A.

2009-07-01

We give a comparison of the efficiency of three alternative decomposition schemes for the approximate solution of multi-term fractional differential equations using the Caputo form of the fractional derivative. The schemes we compare are based on conversion of the original problem into a system of equations. We review alternative approaches and consider how the most appropriate numerical scheme may be chosen to solve a particular equation.

Fractional thermoelasticity

CERN Document Server

Povstenko, Yuriy

2015-01-01

This book is devoted to fractional thermoelasticity, i.e. thermoelasticity based on the heat conduction equation with differential operators of fractional order. Readers will discover how time-fractional differential operators describe memory effects and space-fractional differential operators deal with the long-range interaction. Fractional calculus, generalized Fourier law, axisymmetric and central symmetric problems and many relevant equations are featured in the book. The latest developments in the field are included and the reader is brought up to date with current research.  The book contains a large number of figures, to show the characteristic features of temperature and stress distributions and to represent the whole spectrum of order of fractional operators.  This work presents a picture of the state-of-the-art of fractional thermoelasticity and is suitable for specialists in applied mathematics, physics, geophysics, elasticity, thermoelasticity and engineering sciences. Corresponding sections of ...

Phase 2 Trial of Accelerated, Hypofractionated Whole-Breast Irradiation of 39 Gy in 13 Fractions Followed by a Tumor Bed Boost Sequentially Delivering 9 Gy in 3 Fractions in Early-Stage Breast Cancer

International Nuclear Information System (INIS)

Kim, Ja Young; Jung, So-Youn; Lee, Seeyoun; Kang, Han-Sung; Lee, Eun Sook; Park, In Hae; Lee, Keun Seok; Ro, Jungsil; Lee, Nam Kwon; Shin, Kyung Hwan

2013-01-01

Purpose: To report a phase 2 trial of accelerated, hypofractionated whole-breast irradiation (AH-WBI) delivered as a daily dose of 3 Gy to the whole breast followed by a tumor bed boost. Methods and Materials: Two hundred seventy-six patients diagnosed with breast cancer (pT1-2 and pN0-1a) who had undergone breast-conserving surgery in which the operative margins were negative were treated with AH-WBI delivered as 39 Gy in 13 fractions of 3 Gy to the whole breast once daily over 5 consecutive working days, and 9 Gy in 3 sequential fractions of 3 Gy to a lumpectomy cavity, all within 3.2 weeks. Results: After a median follow-up period of 57 months (range: 27-75 months), the rate of 5-year locoregional recurrence was 1.4% (n=4), whereas that of disease-free survival was 97.4%. No grade 3 skin toxicity was reported during the follow-up period. Qualitative physician cosmetic assessments of good or excellent were noted in 82% of the patients at 2 months after the completion of AH-WBI. The global cosmetic outcome did not worsen over time, and a good or excellent cosmetic outcome was reported in 82% of the patients at 3 years. The mean pretreatment percentage breast retraction assessment was 12.00 (95% confidence interval [CI]: 11.14-12.86). The mean value of percentage breast retraction assessment increased to 13.99 (95% CI: 12.17-15.96) after 1 year and decreased to 13.54 (95% CI: 11.84-15.46) after 3 years but was not significant (P>.05). Conclusions: AH-WBI consisting of 39 Gy in 13 fractions followed by a tumor bed boost sequentially delivering 9 Gy in 3 fractions can be delivered with excellent disease control and tolerable skin toxicity in patients with early-stage breast cancer after breast-conserving surgery

On Impulsive Boundary Value Problems of Fractional Differential Equations with Irregular Boundary Conditions

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Guotao Wang

2012-01-01

Full Text Available We study nonlinear impulsive differential equations of fractional order with irregular boundary conditions. Some existence and uniqueness results are obtained by applying standard fixed-point theorems. For illustration of the results, some examples are discussed.

An Accurate Approximate-Analytical Technique for Solving Time-Fractional Partial Differential Equations

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M. Bishehniasar

2017-01-01

Full Text Available The demand of many scientific areas for the usage of fractional partial differential equations (FPDEs to explain their real-world systems has been broadly identified. The solutions may portray dynamical behaviors of various particles such as chemicals and cells. The desire of obtaining approximate solutions to treat these equations aims to overcome the mathematical complexity of modeling the relevant phenomena in nature. This research proposes a promising approximate-analytical scheme that is an accurate technique for solving a variety of noninteger partial differential equations (PDEs. The proposed strategy is based on approximating the derivative of fractional-order and reducing the problem to the corresponding partial differential equation (PDE. Afterwards, the approximating PDE is solved by using a separation-variables technique. The method can be simply applied to nonhomogeneous problems and is proficient to diminish the span of computational cost as well as achieving an approximate-analytical solution that is in excellent concurrence with the exact solution of the original problem. In addition and to demonstrate the efficiency of the method, it compares with two finite difference methods including a nonstandard finite difference (NSFD method and standard finite difference (SFD technique, which are popular in the literature for solving engineering problems.

Geometrical explanation of the fractional complex transform and derivative chain rule for fractional calculus

International Nuclear Information System (INIS)

He, Ji-Huan; Elagan, S.K.; Li, Z.B.

2012-01-01

The fractional complex transform is suggested to convert a fractional differential equation with Jumarie's modification of Riemann–Liouville derivative into its classical differential partner. Understanding the fractional complex transform and the chain rule for fractional calculus are elucidated geometrically. -- Highlights: ► The chain rule for fractional calculus is invalid, a counter example is given. ► The fractional complex transform is explained geometrically. ► Fractional equations can be converted into differential equations.

Series expansion solutions for the multi-term time and space fractional partial differential equations in two- and three-dimensions

Science.gov (United States)

Ye, H.; Liu, F.; Turner, I.; Anh, V.; Burrage, K.

2013-09-01

Fractional partial differential equations with more than one fractional derivative in time describe some important physical phenomena, such as the telegraph equation, the power law wave equation, or the Szabo wave equation. In this paper, we consider two- and three-dimensional multi-term time and space fractional partial differential equations. The multi-term time-fractional derivative is defined in the Caputo sense, whose order belongs to the interval (1,2],(2,3],(3,4] or (0, m], and the space-fractional derivative is referred to as the fractional Laplacian form. We derive series expansion solutions based on a spectral representation of the Laplacian operator on a bounded region. Some applications are given for the two- and three-dimensional telegraph equation, power law wave equation and Szabo wave equation.

Traveling wave solutions to some nonlinear fractional partial differential equations through the rational (G′/G-expansion method

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Tarikul Islam

2018-03-01

Full Text Available In this article, the analytical solutions to the space-time fractional foam drainage equation and the space-time fractional symmetric regularized long wave (SRLW equation are successfully examined by the recently established rational (G′/G-expansion method. The suggested equations are reduced into the nonlinear ordinary differential equations with the aid of the fractional complex transform. Consequently, the theories of the ordinary differential equations are implemented effectively. Three types closed form traveling wave solutions, such as hyperbolic function, trigonometric function and rational, are constructed by using the suggested method in the sense of conformable fractional derivative. The obtained solutions might be significant to analyze the depth and spacing of parallel subsurface drain and small-amplitude long wave on the surface of the water in a channel. It is observed that the performance of the rational (G′/G-expansion method is reliable and will be used to establish new general closed form solutions for any other NPDEs of fractional order.

Dynamic flow-through sequential extraction for assessment of fractional transformation and inter-element associations of arsenic in stabilized soil and sludge

International Nuclear Information System (INIS)

Buanuam, Janya; Wennrich, Rainer

2010-01-01

A dynamic flow-through extraction system was applied for the first time to ascertain the fractional transformation and inter-element associations of arsenic in stabilized environmental solids, as exemplified by the partitioning of soil and sludge stabilized with three additives, namely MnO 2 , Ca(OH) 2 and FeSO 4 . The extraction system used not only gave fractionation data, but also the extraction profiles (extractograms) which were used for investigation of the breaking down of phases, kinetic releasing of As and elemental association between As and inorganic additives. Five geochemical fractions of As were elucidated by accommodation in the flow manifold of a modified Wenzel's sequential extraction scheme, well established for fractionation of arsenic. The results revealed that MnO 2 and FeSO 4 have a slight effect on As phase transformation for soil and sludge samples amended for one week whereas the addition of Ca(OH) 2 increases As mobility due to the desorption of As from the solid Fe-oxides phase. The significant change in fractional transformation after 8 weeks of incubation can be seen in MnO 2 -treated soil. There was an increase of 17% in the non-mobilizable As fraction in MnO 2 -treated soil. From extractograms, arsenic in untreated soil was found to be rapidly leached and concurrently released with Fe. This may be evidence that the release of As is dependent on the dissolution of amorphous Fe oxides. In MnO 2 -treated soil, a strong affinity was observed between Mn and As in the amorphous Fe/Al oxides fraction, and this plays an important role in slowing down the kinetics of As releasing.

Fractionation and Mobility of Thallium in Volcanic Ashes after Eruption of Eyjafjallajökull (2010) in Iceland.

Science.gov (United States)

Karbowska, Bozena; Zembrzuski, Wlodzimierz

2016-07-01

Volcanic ash contains thallium (Tl), which is highly toxic to the biosphere. The aim of this study was to determine the Tl concentration in fractions of volcanic ash samples originating from the Eyjafjallajökull volcano. A sequential extraction scheme allowed for a study of element migration in the environment. Differential pulse anodic stripping voltammetry using a flow measuring system was selected as the analytical method to determine Tl content. The highest average content of Tl in volcanic ash was determined in the fraction entrapped in the aluminosilicate matrix (0.329 µg g(-1)), followed by the oxidizable fraction (0.173 µg g(-1)). The lowest content of Tl was found in the water soluble fraction (0.001 µg g(-1)); however, this fraction is important due to the fact that Tl redistribution among all the fractions occurs through the aqueous phase.

Successful Treatment of Tattoo-Induced Pseudolymphoma with Sequential Ablative Fractional Resurfacing Followed by Q-Switched Nd: YAG 532 nm Laser

Science.gov (United States)

Lucinda, Tan Siyun; Hazel, Oon Hwee Boon; Joyce, Lee Siong Siong; Hon, Chua Sze

2013-01-01

Decorative tattooing has been linked with a range of complications, with pseudolymphoma being unusual and challenging to manage. We report a case of tattoo-induced pseudolymphoma, who failed treatment with potent topical and intralesional steroids. She responded well to sequential treatment with ablative fractional resurfacing (AFR) followed by Q-Switched (QS) Nd:YAG 532 nm laser. Interestingly, we managed to document the clearance of her tattoo pigments after laser treatments on histology and would like to highlight the use of special stains such as the Grocott's Methenamine Silver (GMS) stain as a useful method to assess the presence of tattoo pigment in cases where dense inflammatory infiltrates are present. PMID:24470721

Existence results for fractional integro-differential inclusions with state-dependent delay

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Siracusa Giovana

2017-10-01

Full Text Available In this paper we are concerned with a class of abstract fractional integro-differential inclusions with infinite state-dependent delay. Our approach is based on the existence of a resolvent operator for the homogeneous equation.We establish the existence of mild solutions using both contractive maps and condensing maps. Finally, an application to the theory of heat conduction in materials with memory is given.

S.M.P. SEQUENTIAL MATHEMATICS PROGRAM.

Science.gov (United States)

CICIARELLI, V; LEONARD, JOSEPH

A SEQUENTIAL MATHEMATICS PROGRAM BEGINNING WITH THE BASIC FUNDAMENTALS ON THE FOURTH GRADE LEVEL IS PRESENTED. INCLUDED ARE AN UNDERSTANDING OF OUR NUMBER SYSTEM, AND THE BASIC OPERATIONS OF WORKING WITH WHOLE NUMBERS--ADDITION, SUBTRACTION, MULTIPLICATION, AND DIVISION. COMMON FRACTIONS ARE TAUGHT IN THE FIFTH, SIXTH, AND SEVENTH GRADES. A…

Animal manure phosphorus characterization by sequential chemical fractionation, release kinetics and 31P-NMR analysis

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Tales Tiecher

2014-10-01

Full Text Available Phosphate release kinetics from manures are of global interest because sustainable plant nutrition with phosphate will be a major concern in the future. Although information on the bioavailability and chemical composition of P present in manure used as fertilizer are important to understand its dynamics in the soil, such studies are still scarce. Therefore, P extraction was evaluated in this study by sequential chemical fractionation, desorption with anion-cation exchange resin and 31P nuclear magnetic resonance (31P-NMR spectroscopy to assess the P forms in three different dry manure types (i.e. poultry, cattle and swine manure. All three methods showed that the P forms in poultry, cattle and swine dry manures are mostly inorganic and highly bioavailable. The estimated P pools showed that organic and recalcitrant P forms were negligible and highly dependent on the Ca:P ratio in manures. The results obtained here showed that the extraction of P with these three different methods allows a better understanding and complete characterization of the P pools present in the manures.

Fractional Differential Equation

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Moustafa El-Shahed

2007-01-01

where 2<α<3 is a real number and D0+α is the standard Riemann-Liouville fractional derivative. Our analysis relies on Krasnoselskiis fixed point theorem of cone preserving operators. An example is also given to illustrate the main results.

Identification of fractional-order systems via a switching differential evolution subject to noise perturbations

Energy Technology Data Exchange (ETDEWEB)

Zhu, Wu, E-mail: dtzhuwu@gmail.com [College of Information Science and Technology, Donghua University, Shanghai 201620 (China); Fang, Jian-an [College of Information Science and Technology, Donghua University, Shanghai 201620 (China); Tang, Yang, E-mail: yang.tang@pik-potsdam.de [Institute of Physics, Humboldt University, Berlin 12489 (Germany); Potsdam Institute for Climate Impact Research, Potsdam 14415 (Germany); Research Institute for Intelligent Control and System, Harbin Institute of Technology, Harbin 150006 (China); Zhang, Wenbing [Institute of Textiles and Clothing, The Hong Kong Polytechnic University, Hong Kong (China); Xu, Yulong [College of Information Science and Technology, Donghua University, Shanghai 201620 (China)

2012-10-01

In this Letter, a differential evolution variant, called switching DE (SDE), has been employed to estimate the orders and parameters in incommensurate fractional-order chaotic systems. The proposed algorithm includes a switching population utilization strategy, where the population size is adjusted dynamically based on the solution-searching status. Thus, this adaptive control method realizes the identification of fractional-order Lorenz, Lü and Chen systems in both deterministic and stochastic environments, respectively. Numerical simulations are provided, where comparisons are made with five other State-of-the-Art evolutionary algorithms (EAs) to verify the effectiveness of the proposed method. -- Highlights: ► Switching population utilization strategy is applied for differential evolution. ► The parameters are estimated in both deterministic and stochastic environments. ► Comparisons with five other EAs verify the effectiveness of the proposed method.

Identification of fractional-order systems via a switching differential evolution subject to noise perturbations

International Nuclear Information System (INIS)

Zhu, Wu; Fang, Jian-an; Tang, Yang; Zhang, Wenbing; Xu, Yulong

2012-01-01

In this Letter, a differential evolution variant, called switching DE (SDE), has been employed to estimate the orders and parameters in incommensurate fractional-order chaotic systems. The proposed algorithm includes a switching population utilization strategy, where the population size is adjusted dynamically based on the solution-searching status. Thus, this adaptive control method realizes the identification of fractional-order Lorenz, Lü and Chen systems in both deterministic and stochastic environments, respectively. Numerical simulations are provided, where comparisons are made with five other State-of-the-Art evolutionary algorithms (EAs) to verify the effectiveness of the proposed method. -- Highlights: ► Switching population utilization strategy is applied for differential evolution. ► The parameters are estimated in both deterministic and stochastic environments. ► Comparisons with five other EAs verify the effectiveness of the proposed method.

Integral Boundary Value Problems for Fractional Impulsive Integro Differential Equations in Banach Spaces

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A. Anguraj

2014-02-01

Full Text Available We study in this paper,the existence of solutions for fractional integro differential equations with impulsive and integral conditions by using fixed point method. We establish the Sufficient conditions and unique solution for given problem. An Example is also explained to the main results.

Positive solutions of fractional differential equations with derivative terms

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Cuiping Cheng

2012-11-01

Full Text Available In this article, we are concerned with the existence of positive solutions for nonlinear fractional differential equation whose nonlinearity contains the first-order derivative, $$displaylines{ D_{0^+}^{alpha}u(t+f(t,u(t,u'(t=0,quad tin (0,1,; n-14 $ $(ninmathbb{N}$, $D_{0^+}^{alpha}$ is the standard Riemann-Liouville fractional derivative of order $alpha$ and $f(t,u,u':[0,1] imes [0,inftyimes(-infty,+infty o [0,infty$ satisfies the Caratheodory type condition. Sufficient conditions are obtained for the existence of at least one or two positive solutions by using the nonlinear alternative of the Leray-Schauder type and Krasnosel'skii's fixed point theorem. In addition, several other sufficient conditions are established for the existence of at least triple, n or 2n-1 positive solutions. Two examples are given to illustrate our theoretical results.

Differential branching fraction and angular analysis of the $B^+ \\to K^+ \\mu^+ \\mu^-$ decay

CERN Document Server

INSPIRE-00258707; Abellan Beteta, C; Adametz, A; Adeva, B; Adinolfi, M; Adrover, C; Affolder, A; Ajaltouni, Z; Albrecht, J; Alessio, F; Alexander, M; Ali, S; Alkhazov, G; Alvarez Cartelle, P; Alves Jr, A A; Amato, S; Amhis, Y; Anderlini, L; Anderson, J; Appleby, R B; Aquines Gutierrez, O; Archilli, F; Artamonov, A; Artuso, M; Aslanides, E; Auriemma, G; Bachmann, S; Back, J J; Baesso, C; Baldini, W; Barlow, R J; Barschel, C; Barsuk, S; Barter, W; Bates, A; Bauer, Th; Bay, A; Beddow, J; Bediaga, I; Belogurov, S; Belous, K; Belyaev, I; Ben-Haim, E; Benayoun, M; Bencivenni, G; Benson, S; Benton, J; Berezhnoy, A; Bernet, R; Bettler, M -O; van Beuzekom, M; Bien, A; Bifani, S; Bird, T; Bizzeti, A; Bjørnstad, P M; Blake, T; Blanc, F; Blanks, C; Blouw, J; Blusk, S; Bobrov, A; Bocci, V; Bondar, A; Bondar, N; Bonivento, W; Borghi, S; Borgia, A; Bowcock, T J V; Bowen, E E; Bozzi, C; Brambach, T; van den Brand, J; Bressieux, J; Brett, D; Britsch, M; Britton, T; Brook, N H; Brown, H; Büchler-Germann, A; Burducea, I; Bursche, A; Buytaert, J; Cadeddu, S; Callot, O; Calvi, M; Calvo Gomez, M; Camboni, A; Campana, P; Carbone, A; Carboni, G; Cardinale, R; Cardini, A; Carson, L; Carvalho Akiba, K; Casse, G; Cattaneo, M; Cauet, Ch; Charles, M; Charpentier, Ph; Chen, P; Chiapolini, N; Chrzaszcz, M; Ciba, K; Cid Vidal, X; Ciezarek, G; Clarke, P E L; Clemencic, M; Cliff, H V; Closier, J; Coca, C; Coco, V; Cogan, J; Cogneras, E; Collins, P; Comerma-Montells, A; Contu, A; Cook, A; Coombes, M; Corti, G; Couturier, B; Cowan, G A; Craik, D; Cunliffe, S; Currie, R; D'Ambrosio, C; David, P; David, P N Y; De Bonis, I; De Bruyn, K; De Capua, S; De Cian, M; De Miranda, J M; De Paula, L; De Simone, P; Decamp, D; Deckenhoff, M; Degaudenzi, H; Del Buono, L; Deplano, C; Derkach, D; Deschamps, O; Dettori, F; Di Canto, A; Dickens, J; Dijkstra, H; Diniz Batista, P; Domingo Bonal, F; Donleavy, S; Dordei, F; Dosil Suárez, A; Dossett, D; Dovbnya, A; Dupertuis, F; Dzhelyadin, R; Dziurda, A; Dzyuba, A; Easo, S; Egede, U; Egorychev, V; Eidelman, S; van Eijk, D; Eisenhardt, S; Ekelhof, R; Eklund, L; El Rifai, I; Elsasser, Ch; Elsby, D; Esperante Pereira, D; Falabella, A; Färber, C; Fardell, G; Farinelli, C; Farry, S; Fave, V; Fernandez Albor, V; Ferreira Rodrigues, F; Ferro-Luzzi, M; Filippov, S; Fitzpatrick, C; Fontana, M; Fontanelli, F; Forty, R; Francisco, O; Frank, M; Frei, C; Frosini, M; Furcas, S; Gallas Torreira, A; Galli, D; Gandelman, M; Gandini, P; Gao, Y; Garnier, J-C; Garofoli, J; Garra Tico, J; Garrido, L; Gaspar, C; Gauld, R; Gersabeck, E; Gersabeck, M; Gershon, T; Ghez, Ph; Gibson, V; Gligorov, V V; Göbel, C; Golubkov, D; Golutvin, A; Gomes, A; Gordon, H; Grabalosa Gándara, M; Graciani Diaz, R; Granado Cardoso, L A; Graugés, E; Graziani, G; Grecu, A; Greening, E; Gregson, S; Grünberg, O; Gui, B; Gushchin, E; Guz, Yu; Gys, T; Hadjivasiliou, C; Haefeli, G; Haen, C; Haines, S C; Hall, S; Hampson, T; Hansmann-Menzemer, S; Harnew, N; Harnew, S T; Harrison, J; Harrison, P F; Hartmann, T; He, J; Heijne, V; Hennessy, K; Henrard, P; Hernando Morata, J A; van Herwijnen, E; Hicks, E; Hill, D; Hoballah, M; Hopchev, P; Hulsbergen, W; Hunt, P; Huse, T; Hussain, N; Huston, R S; Hutchcroft, D; Hynds, D; Iakovenko, V; Ilten, P; Imong, J; Jacobsson, R; Jaeger, A; Jahjah Hussein, M; Jans, E; Jansen, F; Jaton, P; Jean-Marie, B; Jing, F; John, M; Johnson, D; Jones, C R; Jost, B; Kaballo, M; Kandybei, S; Karacson, M; Karbach, T M; Keaveney, J; Kenyon, I R; Kerzel, U; Ketel, T; Keune, A; Khanji, B; Kim, Y M; Kochebina, O; Komarov, V; Koopman, R F; Koppenburg, P; Korolev, M; Kozlinskiy, A; Kravchuk, L; Kreplin, K; Kreps, M; Krocker, G; Krokovny, P; Kruse, F; Kucharczyk, M; Kudryavtsev, V; Kvaratskheliya, T; La Thi, V N; Lacarrere, D; Lafferty, G; Lai, A; Lambert, D; Lambert, R W; Lanciotti, E; Lanfranchi, G; Langenbruch, C; Latham, T; Lazzeroni, C; Le Gac, R; van Leerdam, J; Lees, J -P; Lefèvre, R; Leflat, A; Lefrançois, J; Leroy, O; Lesiak, T; Li, Y; Li Gioi, L; Liles, M; Lindner, R; Linn, C; Liu, B; Liu, G; von Loeben, J; Lopes, J H; Lopez Asamar, E; Lopez-March, N; Lu, H; Luisier, J; Mac Raighne, A; Machefert, F; Machikhiliyan, I V; Maciuc, F; Maev, O; Magnin, J; Maino, M; Malde, S; Manca, G; Mancinelli, G; Mangiafave, N; Marconi, U; Märki, R; Marks, J; Martellotti, G; Martens, A; Martin, L; Martín Sánchez, A; Martinelli, M; Martinez Santos, D; Massafferri, A; Mathe, Z; Matteuzzi, C; Matveev, M; Maurice, E; Mazurov, A; McCarthy, J; McGregor, G; McNulty, R; Meissner, M; Merk, M; Merkel, J; Milanes, D A; Minard, M -N; Molina Rodriguez, J; Monteil, S; Moran, D; Morawski, P; Mountain, R; Mous, I; Muheim, F; Müller, K; Muresan, R; Muryn, B; Muster, B; Mylroie-Smith, J; Naik, P; Nakada, T; Nandakumar, R; Nasteva, I; Needham, M; Neufeld, N; Nguyen, A D; Nguyen-Mau, C; Nicol, M; Niess, V; Nikitin, N; Nikodem, T; Nomerotski, A; Novoselov, A; Oblakowska-Mucha, A; Obraztsov, V; Oggero, S; Ogilvy, S; Okhrimenko, O; Oldeman, R; Orlandea, M; Otalora Goicochea, J M; Owen, P; Pal, B K; Palano, A; Palutan, M; Panman, J; Papanestis, A; Pappagallo, M; Parkes, C; Parkinson, C J; Passaleva, G; Patel, G D; Patel, M; Patrick, G N; Patrignani, C; Pavel-Nicorescu, C; Pazos Alvarez, A; Pellegrino, A; Penso, G; Pepe Altarelli, M; Perazzini, S; Perego, D L; Perez Trigo, E; Pérez-Calero Yzquierdo, A; Perret, P; Perrin-Terrin, M; Pessina, G; Petridis, K; Petrolini, A; Phan, A; Picatoste Olloqui, E; Pie Valls, B; Pietrzyk, B; Pilař, T; Pinci, D; Playfer, S; Plo Casasus, M; Polci, F; Polok, G; Poluektov, A; Polycarpo, E; Popov, D; Popovici, B; Potterat, C; Powell, A; Prisciandaro, J; Pugatch, V; Puig Navarro, A; Qian, W; Rademacker, J H; Rakotomiaramanana, B; Rangel, M S; Raniuk, I; Rauschmayr, N; Raven, G; Redford, S; Reid, M M; dos Reis, A C; Ricciardi, S; Richards, A; Rinnert, K; Rives Molina, V; Roa Romero, D A; Robbe, P; Rodrigues, E; Rodriguez Perez, P; Rogers, G J; Roiser, S; Romanovsky, V; Romero Vidal, A; Rouvinet, J; Ruf, T; Ruiz, H; Sabatino, G; Saborido Silva, J J; Sagidova, N; Sail, P; Saitta, B; Salzmann, C; Sanmartin Sedes, B; Sannino, M; Santacesaria, R; Santamarina Rios, C; Santinelli, R; Santovetti, E; Sapunov, M; Sarti, A; Satriano, C; Satta, A; Savrie, M; Schaack, P; Schiller, M; Schindler, H; Schleich, S; Schlupp, M; Schmelling, M; Schmidt, B; Schneider, O; Schopper, A; Schune, M -H; Schwemmer, R; Sciascia, B; Sciubba, A; Seco, M; Semennikov, A; Senderowska, K; Sepp, I; Serra, N; Serrano, J; Seyfert, P; Shapkin, M; Shapoval, I; Shatalov, P; Shcheglov, Y; Shears, T; Shekhtman, L; Shevchenko, O; Shevchenko, V; Shires, A; Silva Coutinho, R; Skwarnicki, T; Smith, N A; Smith, E; Smith, M; Sobczak, K; Soler, F J P; Solomin, A; Soomro, F; Souza, D; Souza De Paula, B; Spaan, B; Sparkes, A; Spradlin, P; Stagni, F; Stahl, S; Steinkamp, O; Stoica, S; Stone, S; Storaci, B; Straticiuc, M; Straumann, U; Subbiah, V K; Swientek, S; Szczekowski, M; Szczypka, P; Szumlak, T; T'Jampens, S; Teklishyn, M; Teodorescu, E; Teubert, F; Thomas, C; Thomas, E; van Tilburg, J; Tisserand, V; Tobin, M; Tolk, S; Topp-Joergensen, S; Torr, N; Tournefier, E; Tourneur, S; Tran, M T; Tsaregorodtsev, A; Tuning, N; Ubeda Garcia, M; Ukleja, A; Urner, D; Uwer, U; Vagnoni, V; Valenti, G; Vazquez Gomez, R; Vazquez Regueiro, P; Vecchi, S; Velthuis, J J; Veltri, M; Veneziano, G; Vesterinen, M; Viaud, B; Videau, I; Vieira, D; Vilasis-Cardona, X; Visniakov, J; Vollhardt, A; Volyanskyy, D; Voong, D; Vorobyev, A; Vorobyev, V; Voss, H; Voß, C; Waldi, R; Wallace, R; Wandernoth, S; Wang, J; Ward, D R; Watson, N K; Webber, A D; Websdale, D; Whitehead, M; Wicht, J; Wiedner, D; Wiggers, L; Wilkinson, G; Williams, M P; Williams, M; Wilson, F F; Wishahi, J; Witek, M; Witzeling, W; Wotton, S A; Wright, S; Wu, S; Wyllie, K; Xie, Y; Xing, F; Xing, Z; Yang, Z; Young, R; Yuan, X; Yushchenko, O; Zangoli, M; Zavertyaev, M; Zhang, F; Zhang, L; Zhang, W C; Zhang, Y; Zhelezov, A; Zhong, L; Zvyagin, A

2013-01-01

The angular distribution and differential branching fraction of the decay $B^+ \\to K^+ \\mu^+\\mu^-$ are studied with a dataset corresponding to 1.0 fb$^{-1}$ of integrated luminosity, collected by the LHCb experiment. The angular distribution is measured in bins of dimuon invariant mass squared and found to be consistent with Standard Model expectations. Integrating the differential branching fraction over the full dimuon invariant mass range yields a total branching fraction of $B(B^+ \\to K^+ \\mu^+\\mu^-) = (4.36 ± 0.15 ± 0.18) \\times 10^{−7}$. These measurements are the most precise to date of the $B^+ \\to K^+ \\mu^+\\mu^-$ decay.

Spectral finite element methods for solving fractional differential equations with applications in anomalous transport

Energy Technology Data Exchange (ETDEWEB)

Carella, Alfredo Raul

2012-09-15

Quantifying species transport rates is a main concern in chemical and petrochemical industries. In particular, the design and operation of many large-scale industrial chemical processes is as much dependent on diffusion as it is on reaction rates. However, the existing diffusion models sometimes fail to predict experimentally observed behaviors and their accuracy is usually insufficient for process optimization purposes. Fractional diffusion models offer multiple possibilities for generalizing Flick's law in a consistent manner in order to account for history dependence and nonlocal effects. These models have not been extensively applied to the study of real systems, mainly due to their computational cost and mathematical complexity. A least squares spectral formulation was developed for solving fractional differential equations. The proposed method was proven particularly well-suited for dealing with the numerical difficulties inherent to fractional differential operators. The practical implementation was explained in detail in order to enhance reproducibility, and directions were specified for extending it to multiple dimensions and arbitrarily shaped domains. A numerical framework based on the least-squares spectral element method was developed for studying and comparing anomalous diffusion models in pellets. This simulation tool is capable of solving arbitrary integro-differential equations and can be effortlessly adapted to various problems in any number of dimensions. Simulations of the flow around a cylindrical particle were achieved by extending the functionality of the developed framework. A test case was analyzed by coupling the boundary condition yielded by the fluid model with two families of anomalous diffusion models: hyperbolic diffusion and fractional diffusion. Qualitative guidelines for determining the suitability of diffusion models can be formulated by complementing experimental data with the results obtained from this approach.(Author)

Element fractionation by sequential extraction in a soil with high carbonate content

International Nuclear Information System (INIS)

Sulkowski, Margareta; Hirner, Alfred V.

2006-01-01

The influence of carbonate and other buffering substances in soils on the results of a 3-step sequential extraction procedure (BCR) used for metal fractionation was investigated. Deviating from the original extraction scheme, where the extracts are analysed only for a limited number of metals, almost all elements in the soils were quantified by X-ray fluorescence spectroscopy, in the initial samples as well as in the residues of all extraction steps. Additionally, the mineral contents were determined by X-ray diffractometry. Using this methodology, it was possible to correlate changes in soil composition caused by the extraction procedure with the release of elements. Furthermore, the pH values of all extracts were monitored, and certain extraction steps were repeated until no significant pH-rise occurred. A soil with high dolomite content (27%) and a carbonate free soil were extracted. Applying the original BCR-sequence to the calcareous soil, carbonate was found in the residues of the first two steps and extract pH-values rose by around two units in the first and second step, caused mainly by carbonate dissolution. This led to wrong assignment of the carbonate elements Ca, Mg, Sr, Ba, and also to decreased desorption and increased re-adsorption of ions in those steps. After repetition of the acetic acid step until extract pH remained low, the carbonate was completely destroyed and the distributions of the elements Ca, Mg, Sr, Ba as well as those of Co, Ni, Cu, Zn and Pb were found to be quite different to those determined in the original extraction. Furthermore, it could be shown that the effectiveness of the reduction process in step two was reduced by increasing pH: Fe oxides were not significantly attacked by the repeated acetic acid treatments, but a 10-fold amount of Fe was mobilized by hydroxylamine hydrochloride after complete carbonate destruction. On the other hand, only small amounts of Fe were released anyway. Even repeated reduction steps did not

Measurements of the S-wave fraction in B-0 -> K+ pi(-) mu(+) mu(-) decays and the B-0 -> K*(892)(0) mu(+) mu(-) differential branching fraction

NARCIS (Netherlands)

Aaij, R.; Adeva, B.; Adinolfi, M.; Ajaltouni, Z.; Akar, S.; Albrecht, J.; Alessio, F.; Alexander, M.; Ali, S.; Alkhazov, G.; Cartelle, P. Alvarez; Alves, A. A.; Amato, S.; Amerio, S.; Amhis, Y.; An, L.; Anderlini, L.; Andreassi, G.; Andreotti, M.; Andrews, J. E.; Appleby, R. B.; Gutierrez, O. Aquines; Archilli, F.; d'Argent, P.; Artamonov, A.; Artuso, M.; Aslanides, E.; Auriemma, G.; Baalouch, M.; Bachmann, S.; Back, J. J.; Badalov, A.; Baesso, C.; Baldini, W.; Barlow, R. J.; Barschel, C.; Barsuk, S.; Barter, W.; Batozskaya, V.; Battista, V.; Beaucourt, L.; Beddow, J.; Bedeschi, F.; Bediaga, I.; Bel, L. J.; Bellee, V.; Dufour, L.; Onderwater, C. J. G.; Pellegrino, A.; Tolk, S.

2016-01-01

A measurement of the differential branching fraction of the decay B-0 -> K* (892)(0) mu(+)mu(-) is presented together with a determination of the S-wave fraction of the K+ pi(-) system in the decay B-0 -> K+ pi-mu(+)mu(-). The analysis is based on pp-collision data corresponding to an integrated

Zinc fractionation in contaminated soils by sequential and single extractions: influence of soil properties and zinc content.

Science.gov (United States)

Voegelin, Andreas; Tokpa, Gerome; Jacquat, Olivier; Barmettler, Kurt; Kretzschmar, Ruben

2008-01-01

We studied the fractionation of zinc (Zn) in 49 contaminated soils as influenced by Zn content and soil properties using a seven-step sequential extraction procedure (F1: NH4NO3; F2: NH4-acetate, pH 6; F3: NH3OHCl, pH 6; F4: NH4-EDTA, pH 4.6; F5: NH4-oxalate, pH 3; F6: NH4-oxalate/ascorbic acid, pH 3; F7: residual). The soils had developed from different geologic materials and covered a wide range in soil pH (4.0-7.3), organic C content (9.3-102 g kg(-1)), and clay content (38-451 g kg(-1)). Input of aqueous Zn with runoff water from electricity towers during 26 to 74 yr resulted in total soil Zn contents of 3.8 to 460 mmol kg(-1). In acidic soils (n = 24; pH soils (n = 25; pH > or =6.0), most Zn was extracted in the mobilizable fraction (F2) and the intermediate fractions (F4 and F5). The extractability of Zn increased with increasing Zn contamination of the soils. The sum of mobile (F1) and mobilizable (F2) Zn was independent of soil pH, the ratio of Zn in F1 over F1+F2 plotted against soil pH, exhibited the typical shape of a pH sorption edge and markedly increased from pH 6 to pH 5, reflecting the increasing lability of mobilizable Zn with decreasing soil pH. In conclusion, the extractability of Zn from soils contaminated with aqueous Zn after decades of aging under field conditions systematically varied with soil pH and Zn content. The same trends are expected to apply to aqueous Zn released from decomposing Zn-bearing contaminants, such as sewage sludge or smelter slag. The systematic trends in Zn fractionation with varying soil pH and Zn content indicate the paramount effect of these two factors on molecular scale Zn speciation. Further research is required to characterize the link between the fractionation and speciation of Zn and to determine how Zn loading and soil physicochemical properties affect Zn speciation in soils.

Successful treatment of tattoo-induced pseudolymphoma with sequential ablative fractional resurfacing followed by Q-switched Nd: Yag 532 nm laser

Directory of Open Access Journals (Sweden)

Tan Siyun Lucinda

2013-01-01

Full Text Available Decorative tattooing has been linked with a range of complications, with pseudolymphoma being unusual and challenging to manage. We report a case of tattoo-induced pseudolymphoma, who failed treatment with potent topical and intralesional steroids. She responded well to sequential treatment with ablative fractional resurfacing (AFR followed by Q-Switched (QS Nd:YAG 532 nm laser. Interestingly, we managed to document the clearance of her tattoo pigments after laser treatments on histology and would like to highlight the use of special stains such as the Grocott′s Methenamine Silver (GMS stain as a useful method to assess the presence of tattoo pigment in cases where dense inflammatory infiltrates are present.

Novel Numerical Methods for Optimal Control Problems Involving Fractional-Order Differential Equations

Science.gov (United States)

2018-03-14

UNIVERSITY OF TECHNOLOGY Final Report 03/14/2018 DISTRIBUTION A: Distribution approved for public release. AF Office Of Scientific Research (AFOSR...optimal control problems involving fractional-order differential equations Wang, Song Curtin University of Technology Kent Street, Bentley WA6102...Article history : Received 3 October 2016 Accepted 26 March 2017 Available online 29 April 2017 Keywords: Hamilton–Jacobi–Bellman equation Financial

α2 Integrin, extracellular matrix metalloproteinase inducer, and matrix metalloproteinase-3 act sequentially to induce differentiation of mouse embryonic stem cells into odontoblast-like cells

International Nuclear Information System (INIS)

Ozeki, Nobuaki; Kawai, Rie; Hase, Naoko; Hiyama, Taiki; Yamaguchi, Hideyuki; Kondo, Ayami; Nakata, Kazuhiko; Mogi, Makio

2015-01-01

We previously reported that interleukin 1β acts via matrix metalloproteinase (MMP)-3 to regulate cell proliferation and suppress apoptosis in α2 integrin-positive odontoblast-like cells differentiated from mouse embryonic stem (ES) cells. Here we characterize the signal cascade underpinning odontoblastic differentiation in mouse ES cells. The expression of α2 integrin, extracellular matrix metalloproteinase inducer (Emmprin), and MMP-3 mRNA and protein were all potently increased during odontoblastic differentiation. Small interfering RNA (siRNA) disruption of the expression of these effectors potently suppressed the expression of the odontoblastic biomarkers dentin sialophosphoprotein, dentin matrix protein-1 and alkaline phosphatase, and blocked odontoblast calcification. Our siRNA, western blot and blocking antibody analyses revealed a unique sequential cascade involving α2 integrin, Emmprin and MMP-3 that drives ES cell differentiation into odontoblasts. This cascade requires the interaction between α2 integrin and Emmprin and is potentiated by exogenous MMP-3. Finally, although odontoblast-like cells potently express α2, α6, αV, β1, and β3, integrins, we confirmed that β1 integrin acts as the trigger for ES cell differentiation, apparently in complex with α2 integrin. These results demonstrate a unique and unanticipated role for an α2 integrin-, Emmprin-, and MMP-3-mediated signaling cascade in driving mouse ES cell differentiation into odontoblast-like cells. - Highlights: • Odontoblast differentiation requires activation of α2 integrin, Emmprin and MMP-3. • α2 integrin, Emmprin and MMP-3 form a sequential signaling cascade. • β1 integrin acts a specific trigger for odontoblast differentiation. • The role of these effectors is highly novel and unanticipated

α2 Integrin, extracellular matrix metalloproteinase inducer, and matrix metalloproteinase-3 act sequentially to induce differentiation of mouse embryonic stem cells into odontoblast-like cells

Energy Technology Data Exchange (ETDEWEB)

Ozeki, Nobuaki; Kawai, Rie; Hase, Naoko; Hiyama, Taiki; Yamaguchi, Hideyuki [Department of Endodontics, School of Dentistry, Aichi Gakuin University, Nagoya, Aichi 464-8651 (Japan); Kondo, Ayami [Department of Medicinal Biochemistry, School of Pharmacy, Aichi Gakuin University, Nagoya 464-8650 (Japan); Nakata, Kazuhiko [Department of Endodontics, School of Dentistry, Aichi Gakuin University, Nagoya, Aichi 464-8651 (Japan); Mogi, Makio, E-mail: makio@dpc.agu.ac.jp [Department of Medicinal Biochemistry, School of Pharmacy, Aichi Gakuin University, Nagoya 464-8650 (Japan)

2015-02-01

We previously reported that interleukin 1β acts via matrix metalloproteinase (MMP)-3 to regulate cell proliferation and suppress apoptosis in α2 integrin-positive odontoblast-like cells differentiated from mouse embryonic stem (ES) cells. Here we characterize the signal cascade underpinning odontoblastic differentiation in mouse ES cells. The expression of α2 integrin, extracellular matrix metalloproteinase inducer (Emmprin), and MMP-3 mRNA and protein were all potently increased during odontoblastic differentiation. Small interfering RNA (siRNA) disruption of the expression of these effectors potently suppressed the expression of the odontoblastic biomarkers dentin sialophosphoprotein, dentin matrix protein-1 and alkaline phosphatase, and blocked odontoblast calcification. Our siRNA, western blot and blocking antibody analyses revealed a unique sequential cascade involving α2 integrin, Emmprin and MMP-3 that drives ES cell differentiation into odontoblasts. This cascade requires the interaction between α2 integrin and Emmprin and is potentiated by exogenous MMP-3. Finally, although odontoblast-like cells potently express α2, α6, αV, β1, and β3, integrins, we confirmed that β1 integrin acts as the trigger for ES cell differentiation, apparently in complex with α2 integrin. These results demonstrate a unique and unanticipated role for an α2 integrin-, Emmprin-, and MMP-3-mediated signaling cascade in driving mouse ES cell differentiation into odontoblast-like cells. - Highlights: • Odontoblast differentiation requires activation of α2 integrin, Emmprin and MMP-3. • α2 integrin, Emmprin and MMP-3 form a sequential signaling cascade. • β1 integrin acts a specific trigger for odontoblast differentiation. • The role of these effectors is highly novel and unanticipated.

Unveiling hidden properties of young star clusters: differential reddening, star-formation spread, and binary fraction

Science.gov (United States)

Bonatto, C.; Lima, E. F.; Bica, E.

2012-04-01

Context. Usually, important parameters of young, low-mass star clusters are very difficult to obtain by means of photometry, especially when differential reddening and/or binaries occur in large amounts. Aims: We present a semi-analytical approach (ASAmin) that, when applied to the Hess diagram of a young star cluster, is able to retrieve the values of mass, age, star-formation spread, distance modulus, foreground and differential reddening, and binary fraction. Methods: The global optimisation method known as adaptive simulated annealing (ASA) is used to minimise the residuals between the observed and simulated Hess diagrams of a star cluster. The simulations are realistic and take the most relevant parameters of young clusters into account. Important features of the simulations are a normal (Gaussian) differential reddening distribution, a time-decreasing star-formation rate, the unresolved binaries, and the smearing effect produced by photometric uncertainties on Hess diagrams. Free parameters are cluster mass, age, distance modulus, star-formation spread, foreground and differential reddening, and binary fraction. Results: Tests with model clusters built with parameters spanning a broad range of values show that ASAmin retrieves the input values with a high precision for cluster mass, distance modulus, and foreground reddening, but they are somewhat lower for the remaining parameters. Given the statistical nature of the simulations, several runs should be performed to obtain significant convergence patterns. Specifically, we find that the retrieved (absolute minimum) parameters converge to mean values with a low dispersion as the Hess residuals decrease. When applied to actual young clusters, the retrieved parameters follow convergence patterns similar to the models. We show how the stochasticity associated with the early phases may affect the results, especially in low-mass clusters. This effect can be minimised by averaging out several twin clusters in the

Boundedness of the solutions for certain classes of fractional differential equations with application to adaptive systems.

Science.gov (United States)

Aguila-Camacho, Norelys; Duarte-Mermoud, Manuel A

2016-01-01

This paper presents the analysis of three classes of fractional differential equations appearing in the field of fractional adaptive systems, for the case when the fractional order is in the interval α ∈(0,1] and the Caputo definition for fractional derivatives is used. The boundedness of the solutions is proved for all three cases, and the convergence to zero of the mean value of one of the variables is also proved. Applications of the obtained results to fractional adaptive schemes in the context of identification and control problems are presented at the end of the paper, including numerical simulations which support the analytical results. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Fractionation of metals by sequential extraction procedures (BCR and Tessier) in soil exposed to fire of wide temperature range

Science.gov (United States)

Fajkovic, Hana; Rončević, Sanda; Nemet, Ivan; Prohić, Esad; Leontić-Vazdar, Dana

2017-04-01

Forest fire presents serious problem, especially in Mediterranean Region. Effects of fire are numerous, from climate change and deforestation to loss of soil organic matter and changes in soil properties. One of the effects, not well documented, is possible redistribution and/or remobilisation of pollutants previously deposited in the soil, due to the new physical and chemical soil properties and changes in equilibrium conditions. For understanding and predicting possible redistribution and/or remobilisation of potential pollutants from soil, affected by fire different in temperature, several laboratory investigations were carried out. To evaluate the influence of organic matter on soil under fire, three soil samples were analysed and compared: (a) the one with added coniferous organic matter; (b) deciduous organic matter (b) and (c) soil without additional organic matter. Type of organic matter is closely related to pH of soil, as pH is influencing the mobility of some pollutants, e.g. metals. For that reason pH was also measured through all experimental steps. Each of mentioned soil samples (a, b and c) were heated at 1+3 different temperatures (25°C, 200°C, 500°C and 850°C). After heating, whereby fire effect on soil was simulated, samples were analysed by BCR protocol with the addition of a first step of sequential extraction procedure by Tessier and analysis of residual by aqua regia. Element fractionation of heavy metals by this procedure was used to determine the amounts of selected elements (Al, Cd, Cr, Co, Cu, Fe, Mn, Ni, Pb and Zn). Selected metal concentrations were determined using inductively coupled plasma atomic emission spectrometer. Further on, loss of organic matter was calculated after each heating procedure as well as the mineral composition. The mineral composition was determined using an X-ray diffraction. From obtained results, it can be concluded that temperature has an influence on concentration of elements in specific step of

A Sequential, Implicit, Wavelet-Based Solver for Multi-Scale Time-Dependent Partial Differential Equations

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Donald A. McLaren

2013-04-01

Full Text Available This paper describes and tests a wavelet-based implicit numerical method for solving partial differential equations. Intended for problems with localized small-scale interactions, the method exploits the form of the wavelet decomposition to divide the implicit system created by the time-discretization into multiple smaller systems that can be solved sequentially. Included is a test on a basic non-linear problem, with both the results of the test, and the time required to calculate them, compared with control results based on a single system with fine resolution. The method is then tested on a non-trivial problem, its computational time and accuracy checked against control results. In both tests, it was found that the method requires less computational expense than the control. Furthermore, the method showed convergence towards the fine resolution control results.

Paradox of enrichment: A fractional differential approach with memory

Science.gov (United States)

Rana, Sourav; Bhattacharya, Sabyasachi; Pal, Joydeep; N'Guérékata, Gaston M.; Chattopadhyay, Joydev

2013-09-01

The paradox of enrichment (PoE) proposed by Rosenzweig [M. Rosenzweig, The paradox of enrichment, Science 171 (1971) 385-387] is still a fundamental problem in ecology. Most of the solutions have been proposed at an individual species level of organization and solutions at community level are lacking. Knowledge of how learning and memory modify behavioral responses to species is a key factor in making a crucial link between species and community levels. PoE resolution via these two organizational levels can be interpreted as a microscopic- and macroscopic-level solution. Fractional derivatives provide an excellent tool for describing this memory and the hereditary properties of various materials and processes. The derivatives can be physically interpreted via two time scales that are considered simultaneously: the ideal, equably flowing homogeneous local time, and the cosmic (inhomogeneous) non-local time. Several mechanisms and theories have been proposed to resolve the PoE problem, but a universally accepted theory is still lacking because most studies have focused on local effects and ignored non-local effects, which capture memory. Here we formulate the fractional counterpart of the Rosenzweig model and analyze the stability behavior of a system. We conclude that there is a threshold for the memory effect parameter beyond which the Rosenzweig model is stable and may be used as a potential agent to resolve PoE from a new perspective via fractional differential equations.

A Modified Generalized Laguerre-Gauss Collocation Method for Fractional Neutral Functional-Differential Equations on the Half-Line

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Ali H. Bhrawy

2014-01-01

Full Text Available The modified generalized Laguerre-Gauss collocation (MGLC method is applied to obtain an approximate solution of fractional neutral functional-differential equations with proportional delays on the half-line. The proposed technique is based on modified generalized Laguerre polynomials and Gauss quadrature integration of such polynomials. The main advantage of the present method is to reduce the solution of fractional neutral functional-differential equations into a system of algebraic equations. Reasonable numerical results are achieved by choosing few modified generalized Laguerre-Gauss collocation points. Numerical results demonstrate the accuracy, efficiency, and versatility of the proposed method on the half-line.

Positive Solutions for System of Nonlinear Fractional Differential Equations in Two Dimensions with Delay

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Azizollah Babakhani

2010-01-01

Full Text Available We investigate the existence and uniqueness of positive solution for system of nonlinear fractional differential equations in two dimensions with delay. Our analysis relies on a nonlinear alternative of Leray-Schauder type and Krasnoselskii's fixed point theorem in a cone.

Thallium in fractions of sediments formed during the 2004 tsunami in Thailand.

Science.gov (United States)

Lukaszewski, Zenon; Karbowska, Bozena; Zembrzuski, Wlodzimierz; Siepak, Marcin

2012-06-01

Thallium is a highly toxic element. Its concentration in sediment fractions from the 2004 tsunami in Thailand was investigated. A modified BCR procedure was used for sequential extraction. Tl was determined by flow injection differential pulse anodic stripping voltammetry. It was found that the majority of thallium in the investigated tsunami sediments (86-97 percent) is entrapped in the alumosilicate parent matter i.e. it is entirely immovable. Only the total destruction of this residual fraction with hydrofluoric acid made this thallium available. The conclusion strongly supports the hypothesis that thallium is mainly entrapped in alumosilicate parent matter. Total thallium concentration in the investigated tsunami sediments was divergent in various samples from 0.37 to 1.13 μg g(-1) and significantly different from the reference area (0.05 μg g(-1)). Tsunami sediment fractions from different sampling points are divergent in terms of total thallium concentration and concentration of mobile thallium. Generally, mobile thallium concentration was growing in sequence: water soluble fractionthallium concentration in the reducible fraction was higher than in the oxidizable fraction. Copyright © 2012 Elsevier Inc. All rights reserved.

Analytical solutions to time-fractional partial differential equations in a two-dimensional multilayer annulus

Science.gov (United States)

Chen, Shanzhen; Jiang, Xiaoyun

2012-08-01

In this paper, analytical solutions to time-fractional partial differential equations in a multi-layer annulus are presented. The final solutions are obtained in terms of Mittag-Leffler function by using the finite integral transform technique and Laplace transform technique. In addition, the classical diffusion equation (α=1), the Helmholtz equation (α→0) and the wave equation (α=2) are discussed as special cases. Finally, an illustrative example problem for the three-layer semi-circular annular region is solved and numerical results are presented graphically for various kind of order of fractional derivative.

Some operational tools for solving fractional and higher integer order differential equations: A survey on their mutual relations

Science.gov (United States)

Kiryakova, Virginia S.

2012-11-01

The Laplace Transform (LT) serves as a basis of the Operational Calculus (OC), widely explored by engineers and applied scientists in solving mathematical models for their practical needs. This transform is closely related to the exponential and trigonometric functions (exp, cos, sin) and to the classical differentiation and integration operators, reducing them to simple algebraic operations. Thus, the classical LT and the OC give useful tool to handle differential equations and systems with constant coefficients. Several generalizations of the LT have been introduced to allow solving, in a similar way, of differential equations with variable coefficients and of higher integer orders, as well as of fractional (arbitrary non-integer) orders. Note that fractional order mathematical models are recently widely used to describe better various systems and phenomena of the real world. This paper surveys briefly some of our results on classes of such integral transforms, that can be obtained from the LT by means of "transmutations" which are operators of the generalized fractional calculus (GFC). On the list of these Laplace-type integral transforms, we consider the Borel-Dzrbashjan, Meijer, Krätzel, Obrechkoff, generalized Obrechkoff (multi-index Borel-Dzrbashjan) transforms, etc. All of them are G- and H-integral transforms of convolutional type, having as kernels Meijer's G- or Fox's H-functions. Besides, some special functions (also being G- and H-functions), among them - the generalized Bessel-type and Mittag-Leffler (M-L) type functions, are generating Gel'fond-Leontiev (G-L) operators of generalized differentiation and integration, which happen to be also operators of GFC. Our integral transforms have operational properties analogous to those of the LT - they do algebrize the G-L generalized integrations and differentiations, and thus can serve for solving wide classes of differential equations with variable coefficients of arbitrary, including non-integer order

Positive nondecreasing solutions for a multi-term fractional-order functional differential equation with integral conditions

OpenAIRE

Ahmed M. A. El-Sayed; Ebtisam O. Bin-Taher

2011-01-01

In this article, we prove the existence of positive nondecreasing solutions for a multi-term fractional-order functional differential equations. We consider Cauchy boundary problems with: nonlocal conditions, two-point boundary conditions, integral conditions, and deviated arguments.

Nonlinear $q$-fractional differential equations with nonlocal and sub-strip type boundary conditions

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Bashir Ahmad

2014-06-01

Full Text Available This paper is concerned with new boundary value problems of nonlinear $q$-fractional differential equations with nonlocal and sub-strip type boundary conditions. Our results are new in the present setting and rely on the contraction mapping principle and a fixed point theorem due to O'Regan. Some illustrative examples are also presented.

Use of sequential extraction to assess metal partitioning in soils

International Nuclear Information System (INIS)

Kaasalainen, Marika; Yli-Halla, Markku

2003-01-01

The state of heavy metal pollution and the mobility of Cd, Cu, Ni, Cr, Pb and Zn were studied in three texturally different agricultural soil profiles near a Cu-Ni smelter in Harjavalta, Finland. The pseudo-total concentrations were determined by an aqua regia procedure. Metals were also determined after division into four fractions by sequential extraction with (1) acetic acid (exchangeable and specifically adsorbed metals), (2) a reducing agent (bound to Fe/Mn hydroxides), (3) an oxidizing agent (bound to soil organic matter) and (4) aqua regia (bound to mineral structures). Fallout from the smelter has increased the concentrations of Cd, Cu and Ni in the topsoil, where 75-90% of Cd, 49-72% of Cu and 22-52% of Ni occurred in the first two fractions. Slight Pb and Zn pollution was evident as well. High proportions of mobile Cd, Cu and Ni also deeper in the sandy soil, closest to the smelter, indicated some downward movement of metals. The hydroxide-bound fraction of Pb dominated in almost all soils and horizons, while Ni, Cr and Zn mostly occurred in mineral structures. Aqua regia extraction is usefully supplemented with sequential extraction, particularly in less polluted soils and in soils that exhibit substantial textural differences within the profiles. - Sequential extraction is most useful with soils with low metal pollutant levels

Bioinspired nanocomplex for spatiotemporal imaging of sequential mRNA expression in differentiating neural stem cells.

Science.gov (United States)

Wang, Zhe; Zhang, Ruili; Wang, Zhongliang; Wang, He-Fang; Wang, Yu; Zhao, Jun; Wang, Fu; Li, Weitao; Niu, Gang; Kiesewetter, Dale O; Chen, Xiaoyuan

2014-12-23

Messenger RNA plays a pivotal role in regulating cellular activities. The expression dynamics of specific mRNA contains substantial information on the intracellular milieu. Unlike the imaging of stationary mRNAs, real-time intracellular imaging of the dynamics of mRNA expression is of great value for investigating mRNA biology and exploring specific cellular cascades. In addition to advanced imaging methods, timely extracellular stimulation is another key factor in regulating the mRNA expression repertoire. The integration of effective stimulation and imaging into a single robust system would significantly improve stimulation efficiency and imaging accuracy, producing fewer unwanted artifacts. In this study, we developed a multifunctional nanocomplex to enable self-activating and spatiotemporal imaging of the dynamics of mRNA sequential expression during the neural stem cell differentiation process. This nanocomplex showed improved enzymatic stability, fast recognition kinetics, and high specificity. With a mechanism regulated by endogenous cell machinery, this nanocomplex realized the successive stimulating motif release and the dynamic imaging of chronological mRNA expression during neural stem cell differentiation without the use of transgenetic manipulation. The dynamic imaging montage of mRNA expression ultimately facilitated genetic heterogeneity analysis. In vivo lateral ventricle injection of this nanocomplex enabled endogenous neural stem cell activation and labeling at their specific differentiation stages. This nanocomplex is highly amenable as an alternative tool to explore the dynamics of intricate mRNA activities in various physiological and pathological conditions.

Angular analysis and differential branching fraction of the decay $B^0_s\\to\\phi\\mu^+\\mu^-$

CERN Document Server

Aaij, Roel; Adinolfi, Marco; Affolder, Anthony; Ajaltouni, Ziad; Akar, Simon; Albrecht, Johannes; Alessio, Federico; Alexander, Michael; Ali, Suvayu; Alkhazov, Georgy; Alvarez Cartelle, Paula; Alves Jr, Antonio Augusto; Amato, Sandra; Amerio, Silvia; Amhis, Yasmine; An, Liupan; Anderlini, Lucio; Anderson, Jonathan; Andreassi, Guido; Andreotti, Mirco; Andrews, Jason; Appleby, Robert; Aquines Gutierrez, Osvaldo; Archilli, Flavio; d'Argent, Philippe; Artamonov, Alexander; Artuso, Marina; Aslanides, Elie; Auriemma, Giulio; Baalouch, Marouen; Bachmann, Sebastian; Back, John; Badalov, Alexey; Baesso, Clarissa; Baldini, Wander; Barlow, Roger; Barschel, Colin; Barsuk, Sergey; Barter, William; Batozskaya, Varvara; Battista, Vincenzo; Bay, Aurelio; Beaucourt, Leo; Beddow, John; Bedeschi, Franco; Bediaga, Ignacio; Bel, Lennaert; Bellee, Violaine; Belyaev, Ivan; Ben-Haim, Eli; Bencivenni, Giovanni; Benson, Sean; Benton, Jack; Berezhnoy, Alexander; Bernet, Roland; Bertolin, Alessandro; Bettler, Marc-Olivier; van Beuzekom, Martinus; Bien, Alexander; Bifani, Simone; Bird, Thomas; Birnkraut, Alex; Bizzeti, Andrea; Blake, Thomas; Blanc, Frédéric; Blouw, Johan; Blusk, Steven; Bocci, Valerio; Bondar, Alexander; Bondar, Nikolay; Bonivento, Walter; Borghi, Silvia; Borsato, Martino; Bowcock, Themistocles; Bowen, Espen Eie; Bozzi, Concezio; Braun, Svende; Brett, David; Britsch, Markward; Britton, Thomas; Brodzicka, Jolanta; Brook, Nicholas; Bursche, Albert; Buytaert, Jan; Cadeddu, Sandro; Calabrese, Roberto; Calvi, Marta; Calvo Gomez, Miriam; Campana, Pierluigi; Campora Perez, Daniel; Capriotti, Lorenzo; Carbone, Angelo; Carboni, Giovanni; Cardinale, Roberta; Cardini, Alessandro; Carniti, Paolo; Carson, Laurence; Carvalho Akiba, Kazuyoshi; Casse, Gianluigi; Cassina, Lorenzo; Castillo Garcia, Lucia; Cattaneo, Marco; Cauet, Christophe; Cavallero, Giovanni; Cenci, Riccardo; Charles, Matthew; Charpentier, Philippe; Chefdeville, Maximilien; Chen, Shanzhen; Cheung, Shu-Faye; Chiapolini, Nicola; Chrzaszcz, Marcin; Cid Vidal, Xabier; Ciezarek, Gregory; Clarke, Peter; Clemencic, Marco; Cliff, Harry; Closier, Joel; Coco, Victor; Cogan, Julien; Cogneras, Eric; Cogoni, Violetta; Cojocariu, Lucian; Collazuol, Gianmaria; Collins, Paula; Comerma-Montells, Albert; Contu, Andrea; Cook, Andrew; Coombes, Matthew; Coquereau, Samuel; Corti, Gloria; Corvo, Marco; Couturier, Benjamin; Cowan, Greig; Craik, Daniel Charles; Crocombe, Andrew; Cruz Torres, Melissa Maria; Cunliffe, Samuel; Currie, Robert; D'Ambrosio, Carmelo; Dall'Occo, Elena; Dalseno, Jeremy; David, Pieter; Davis, Adam; De Bruyn, Kristof; De Capua, Stefano; De Cian, Michel; De Miranda, Jussara; De Paula, Leandro; De Simone, Patrizia; Dean, Cameron Thomas; Decamp, Daniel; Deckenhoff, Mirko; Del Buono, Luigi; Déléage, Nicolas; Demmer, Moritz; Derkach, Denis; Deschamps, Olivier; Dettori, Francesco; Dey, Biplab; Di Canto, Angelo; Di Ruscio, Francesco; Dijkstra, Hans; Donleavy, Stephanie; Dordei, Francesca; Dorigo, Mirco; Dosil Suárez, Alvaro; Dossett, David; Dovbnya, Anatoliy; Dreimanis, Karlis; Dufour, Laurent; Dujany, Giulio; Dupertuis, Frederic; Durante, Paolo; Dzhelyadin, Rustem; Dziurda, Agnieszka; Dzyuba, Alexey; Easo, Sajan; Egede, Ulrik; Egorychev, Victor; Eidelman, Semen; Eisenhardt, Stephan; Eitschberger, Ulrich; Ekelhof, Robert; Eklund, Lars; El Rifai, Ibrahim; Elsasser, Christian; Ely, Scott; Esen, Sevda; Evans, Hannah Mary; Evans, Timothy; Falabella, Antonio; Färber, Christian; Farinelli, Chiara; Farley, Nathanael; Farry, Stephen; Fay, Robert; Ferguson, Dianne; Fernandez Albor, Victor; Ferrari, Fabio; Ferreira Rodrigues, Fernando; Ferro-Luzzi, Massimiliano; Filippov, Sergey; Fiore, Marco; Fiorini, Massimiliano; Firlej, Miroslaw; Fitzpatrick, Conor; Fiutowski, Tomasz; Fohl, Klaus; Fol, Philip; Fontana, Marianna; Fontanelli, Flavio; Forty, Roger; Francisco, Oscar; Frank, Markus; Frei, Christoph; Frosini, Maddalena; Fu, Jinlin; Furfaro, Emiliano; Gallas Torreira, Abraham; Galli, Domenico; Gallorini, Stefano; Gambetta, Silvia; Gandelman, Miriam; Gandini, Paolo; Gao, Yuanning; García Pardiñas, Julián; Garra Tico, Jordi; Garrido, Lluis; Gascon, David; Gaspar, Clara; Gauld, Rhorry; Gavardi, Laura; Gazzoni, Giulio; Geraci, Angelo; Gerick, David; Gersabeck, Evelina; Gersabeck, Marco; Gershon, Timothy; Ghez, Philippe; Gianelle, Alessio; Gianì, Sebastiana; Gibson, Valerie; Girard, Olivier Göran; Giubega, Lavinia-Helena; Gligorov, V.V.; Göbel, Carla; Golubkov, Dmitry; Golutvin, Andrey; Gomes, Alvaro; Gotti, Claudio; Grabalosa Gándara, Marc; Graciani Diaz, Ricardo; Granado Cardoso, Luis Alberto; Graugés, Eugeni; Graverini, Elena; Graziani, Giacomo; Grecu, Alexandru; Greening, Edward; Gregson, Sam; Griffith, Peter; Grillo, Lucia; Grünberg, Oliver; Gui, Bin; Gushchin, Evgeny; Guz, Yury; Gys, Thierry; Hadavizadeh, Thomas; Hadjivasiliou, Christos; Haefeli, Guido; Haen, Christophe; Haines, Susan; Hall, Samuel; Hamilton, Brian; Han, Xiaoxue; Hansmann-Menzemer, Stephanie; Harnew, Neville; Harnew, Samuel; Harrison, Jonathan; He, Jibo; Head, Timothy; Heijne, Veerle; Hennessy, Karol; Henrard, Pierre; Henry, Louis; Hernando Morata, Jose Angel; van Herwijnen, Eric; Heß, Miriam; Hicheur, Adlène; Hill, Donal; Hoballah, Mostafa; Hombach, Christoph; Hulsbergen, Wouter; Humair, Thibaud; Hussain, Nazim; Hutchcroft, David; Hynds, Daniel; Idzik, Marek; Ilten, Philip; Jacobsson, Richard; Jaeger, Andreas; Jalocha, Pawel; Jans, Eddy; Jawahery, Abolhassan; Jing, Fanfan; John, Malcolm; Johnson, Daniel; Jones, Christopher; Joram, Christian; Jost, Beat; Jurik, Nathan; Kandybei, Sergii; Kanso, Walaa; Karacson, Matthias; Karbach, Moritz; Karodia, Sarah; Kelsey, Matthew; Kenyon, Ian; Kenzie, Matthew; Ketel, Tjeerd; Khanji, Basem; Khurewathanakul, Chitsanu; Klaver, Suzanne; Klimaszewski, Konrad; Kochebina, Olga; Kolpin, Michael; Komarov, Ilya; Koopman, Rose; Koppenburg, Patrick; Kozeiha, Mohamad; Kravchuk, Leonid; Kreplin, Katharina; Kreps, Michal; Krocker, Georg; Krokovny, Pavel; Kruse, Florian; Kucewicz, Wojciech; Kucharczyk, Marcin; Kudryavtsev, Vasily; Kuonen, Axel Kevin; Kurek, Krzysztof; Kvaratskheliya, Tengiz; Lacarrere, Daniel; Lafferty, George; Lai, Adriano; Lambert, Dean; Lanfranchi, Gaia; Langenbruch, Christoph; Langhans, Benedikt; Latham, Thomas; Lazzeroni, Cristina; Le Gac, Renaud; van Leerdam, Jeroen; Lees, Jean-Pierre; Lefèvre, Regis; Leflat, Alexander; Lefrançois, Jacques; Leroy, Olivier; Lesiak, Tadeusz; Leverington, Blake; Li, Yiming; Likhomanenko, Tatiana; Liles, Myfanwy; Lindner, Rolf; Linn, Christian; Lionetto, Federica; Liu, Bo; Liu, Xuesong; Loh, David; Lohn, Stefan; Longstaff, Iain; Lopes, Jose; Lucchesi, Donatella; Lucio Martinez, Miriam; Luo, Haofei; Lupato, Anna; Luppi, Eleonora; Lupton, Oliver; Lusardi, Nicola; Machefert, Frederic; Maciuc, Florin; Maev, Oleg; Maguire, Kevin; Malde, Sneha; Malinin, Alexander; Manca, Giulia; Mancinelli, Giampiero; Manning, Peter Michael; Mapelli, Alessandro; Maratas, Jan; Marchand, Jean François; Marconi, Umberto; Marin Benito, Carla; Marino, Pietro; Märki, Raphael; Marks, Jörg; Martellotti, Giuseppe; Martin, Morgan; Martinelli, Maurizio; Martinez Santos, Diego; Martinez Vidal, Fernando; Martins Tostes, Danielle; Massafferri, André; Matev, Rosen; Mathad, Abhijit; Mathe, Zoltan; Matteuzzi, Clara; Matthieu, Kecke; Mauri, Andrea; Maurin, Brice; Mazurov, Alexander; McCann, Michael; McCarthy, James; McNab, Andrew; McNulty, Ronan; Meadows, Brian; Meier, Frank; Meissner, Marco; Melnychuk, Dmytro; Merk, Marcel; Milanes, Diego Alejandro; Minard, Marie-Noelle; Mitzel, Dominik Stefan; Molina Rodriguez, Josue; Monroy, Ignacio Alberto; Monteil, Stephane; Morandin, Mauro; Morawski, Piotr; Mordà, Alessandro; Morello, Michael Joseph; Moron, Jakub; Morris, Adam Benjamin; Mountain, Raymond; Muheim, Franz; Müller, Janine; Müller, Katharina; Müller, Vanessa; Mussini, Manuel; Muster, Bastien; Naik, Paras; Nakada, Tatsuya; Nandakumar, Raja; Nandi, Anita; Nasteva, Irina; Needham, Matthew; Neri, Nicola; Neubert, Sebastian; Neufeld, Niko; Neuner, Max; Nguyen, Anh Duc; Nguyen, Thi-Dung; Nguyen-Mau, Chung; Niess, Valentin; Niet, Ramon; Nikitin, Nikolay; Nikodem, Thomas; Ninci, Daniele; Novoselov, Alexey; O'Hanlon, Daniel Patrick; Oblakowska-Mucha, Agnieszka; Obraztsov, Vladimir; Ogilvy, Stephen; Okhrimenko, Oleksandr; Oldeman, Rudolf; Onderwater, Gerco; Osorio Rodrigues, Bruno; Otalora Goicochea, Juan Martin; Otto, Adam; Owen, Patrick; Oyanguren, Maria Aranzazu; Palano, Antimo; Palombo, Fernando; Palutan, Matteo; Panman, Jacob; Papanestis, Antonios; Pappagallo, Marco; Pappalardo, Luciano; Pappenheimer, Cheryl; Parkes, Christopher; Passaleva, Giovanni; Patel, Girish; Patel, Mitesh; Patrignani, Claudia; Pearce, Alex; Pellegrino, Antonio; Penso, Gianni; Pepe Altarelli, Monica; Perazzini, Stefano; Perret, Pascal; Pescatore, Luca; Petridis, Konstantinos; Petrolini, Alessandro; Petruzzo, Marco; Picatoste Olloqui, Eduardo; Pietrzyk, Boleslaw; Pilař, Tomas; Pinci, Davide; Pistone, Alessandro; Piucci, Alessio; Playfer, Stephen; Plo Casasus, Maximo; Poikela, Tuomas; Polci, Francesco; Poluektov, Anton; Polyakov, Ivan; Polycarpo, Erica; Popov, Alexander; Popov, Dmitry; Popovici, Bogdan; Potterat, Cédric; Price, Eugenia; Price, Joseph David; Prisciandaro, Jessica; Pritchard, Adrian; Prouve, Claire; Pugatch, Valery; Puig Navarro, Albert; Punzi, Giovanni; Qian, Wenbin; Quagliani, Renato; Rachwal, Bartolomiej; Rademacker, Jonas; Rama, Matteo; Rangel, Murilo; Raniuk, Iurii; Rauschmayr, Nathalie; Raven, Gerhard; Redi, Federico; Reichert, Stefanie; Reid, Matthew; dos Reis, Alberto; Ricciardi, Stefania; Richards, Sophie; Rihl, Mariana; Rinnert, Kurt; Rives Molina, Vincente; Robbe, Patrick; Rodrigues, Ana Barbara; Rodrigues, Eduardo; Rodriguez Lopez, Jairo Alexis; Rodriguez Perez, Pablo; Roiser, Stefan; Romanovsky, Vladimir; Romero Vidal, Antonio; Ronayne, John William; Rotondo, Marcello; Rouvinet, Julien; Ruf, Thomas; Ruiz, Hugo; Ruiz Valls, Pablo; Saborido Silva, Juan Jose; Sagidova, Naylya; Sail, Paul; Saitta, Biagio; Salustino Guimaraes, Valdir; Sanchez Mayordomo, Carlos; Sanmartin Sedes, Brais; Santacesaria, Roberta; Santamarina Rios, Cibran; Santimaria, Marco; Santovetti, Emanuele; Sarti, Alessio; Satriano, Celestina; Satta, Alessia; Saunders, Daniel Martin; Savrina, Darya; Schiller, Manuel; Schindler, Heinrich; Schlupp, Maximilian; Schmelling, Michael; Schmelzer, Timon; Schmidt, Burkhard; Schneider, Olivier; Schopper, Andreas; Schubiger, Maxime; Schune, Marie Helene; Schwemmer, Rainer; Sciascia, Barbara; Sciubba, Adalberto; Semennikov, Alexander; Serra, Nicola; Serrano, Justine; Sestini, Lorenzo; Seyfert, Paul; Shapkin, Mikhail; Shapoval, Illya; Shcheglov, Yury; Shears, Tara; Shekhtman, Lev; Shevchenko, Vladimir; Shires, Alexander; Siddi, Benedetto Gianluca; Silva Coutinho, Rafael; Simi, Gabriele; Sirendi, Marek; Skidmore, Nicola; Skillicorn, Ian; Skwarnicki, Tomasz; Smith, Edmund; Smith, Eluned; Smith, Iwan Thomas; Smith, Jackson; Smith, Mark; Snoek, Hella; Sokoloff, Michael; Soler, Paul; Soomro, Fatima; Souza, Daniel; Souza De Paula, Bruno; Spaan, Bernhard; Spradlin, Patrick; Sridharan, Srikanth; Stagni, Federico; Stahl, Marian; Stahl, Sascha; Steinkamp, Olaf; Stenyakin, Oleg; Sterpka, Christopher Francis; Stevenson, Scott; Stoica, Sabin; Stone, Sheldon; Storaci, Barbara; Stracka, Simone; Straticiuc, Mihai; Straumann, Ulrich; Sun, Liang; Sutcliffe, William; Swientek, Krzysztof; Swientek, Stefan; Syropoulos, Vasileios; Szczekowski, Marek; Szczypka, Paul; Szumlak, Tomasz; T'Jampens, Stephane; Tayduganov, Andrey; Tekampe, Tobias; Teklishyn, Maksym; Tellarini, Giulia; Teubert, Frederic; Thomas, Christopher; Thomas, Eric; van Tilburg, Jeroen; Tisserand, Vincent; Tobin, Mark; Todd, Jacob; Tolk, Siim; Tomassetti, Luca; Tonelli, Diego; Topp-Joergensen, Stig; Torr, Nicholas; Tournefier, Edwige; Tourneur, Stephane; Trabelsi, Karim; Tran, Minh Tâm; Tresch, Marco; Trisovic, Ana; Tsaregorodtsev, Andrei; Tsopelas, Panagiotis; Tuning, Niels; Ukleja, Artur; Ustyuzhanin, Andrey; Uwer, Ulrich; Vacca, Claudia; Vagnoni, Vincenzo; Valenti, Giovanni; Vallier, Alexis; Vazquez Gomez, Ricardo; Vazquez Regueiro, Pablo; Vázquez Sierra, Carlos; Vecchi, Stefania; Velthuis, Jaap; Veltri, Michele; Veneziano, Giovanni; Vesterinen, Mika; Viaud, Benoit; Vieira, Daniel; Vieites Diaz, Maria; Vilasis-Cardona, Xavier; Vollhardt, Achim; Volyanskyy, Dmytro; Voong, David; Vorobyev, Alexey; Vorobyev, Vitaly; Voß, Christian; de Vries, Jacco; Waldi, Roland; Wallace, Charlotte; Wallace, Ronan; Walsh, John; Wandernoth, Sebastian; Wang, Jianchun; Ward, David; Watson, Nigel; Websdale, David; Weiden, Andreas; Whitehead, Mark; Wilkinson, Guy; Wilkinson, Michael; Williams, Mark Richard James; Williams, Matthew; Williams, Mike; Williams, Timothy; Wilson, Fergus; Wimberley, Jack; Wishahi, Julian; Wislicki, Wojciech; Witek, Mariusz; Wormser, Guy; Wotton, Stephen; Wright, Simon; Wyllie, Kenneth; Xie, Yuehong; Xu, Zhirui; Yang, Zhenwei; Yu, Jiesheng; Yuan, Xuhao; Yushchenko, Oleg; Zangoli, Maria; Zavertyaev, Mikhail; Zhang, Liming; Zhang, Yanxi; Zhelezov, Alexey; Zhokhov, Anatoly; Zhong, Liang; Zucchelli, Stefano

2015-09-25

An angular analysis and a measurement of the differential branching fraction of the decay $B^0_s\\to\\phi\\mu^+\\mu^-$ are presented, using data corresponding to an integrated luminosity of $3.0\\, {\\rm fb}^{-1}$ of $pp$ collisions recorded by the LHCb experiment at $\\sqrt{s} = 7$ and $8\\, {\\rm TeV}$. Measurements are reported as a function of $q^{2}$, the square of the dimuon invariant mass and results of the angular analysis are found to be consistent with the Standard Model. In the range $1differential branching fraction is found to be more than $3\\, \\sigma$ below the Standard Model predictions.

Random sequential adsorption of cubes

Science.gov (United States)

Cieśla, Michał; Kubala, Piotr

2018-01-01

Random packings built of cubes are studied numerically using a random sequential adsorption algorithm. To compare the obtained results with previous reports, three different models of cube orientation sampling were used. Also, three different cube-cube intersection algorithms were tested to find the most efficient one. The study focuses on the mean saturated packing fraction as well as kinetics of packing growth. Microstructural properties of packings were analyzed using density autocorrelation function.

All-optical temporal fractional order differentiator using an in-fiber ellipsoidal air-microcavity

Science.gov (United States)

Zhang, Lihong; Sun, Shuqian; Li, Ming; Zhu, Ninghua

2017-12-01

An all-optical temporal fractional order differentiator with ultrabroad bandwidth (~1.6 THz) and extremely simple fabrication is proposed and experimentally demonstrated based on an in-fiber ellipsoidal air-microcavity. The ellipsoidal air-microcavity is fabricated by splicing a single mode fiber (SMF) and a photonic crystal fiber (PCF) together using a simple arc-discharging technology. By changing the arc-discharging times, the propagation loss can be adjusted and then the differentiation order is tuned. A nearly Gaussian-like optical pulse with 3 dB bandwidth of 8 nm is launched into the differentiator and a 0.65 order differentiation of the input pulse is achieved with a processing error of 2.55%. Project supported by the the National Natural Science Foundation of China (Nos. 61522509, 61377002, 61535012), the National High-Tech Research & Development Program of China (No. SS2015AA011002), and the Beijing Natural Science Foundation (No. 4152052). Ming Li was supported in part by the Thousand Young Talent Program.

Existence of Mild Solutions for Impulsive Fractional Integro-Differential Inclusions with State-Dependent Delay

Directory of Open Access Journals (Sweden)

Selvaraj Suganya

2017-01-01

Full Text Available In this manuscript, we implement Bohnenblust–Karlin’s fixed point theorem to demonstrate the existence of mild solutions for a class of impulsive fractional integro-differential inclusions (IFIDI with state-dependent delay (SDD in Banach spaces. An example is provided to illustrate the obtained abstract results.

Positive nondecreasing solutions for a multi-term fractional-order functional differential equation with integral conditions

Directory of Open Access Journals (Sweden)

Ahmed M. A. El-Sayed

2011-12-01

Full Text Available In this article, we prove the existence of positive nondecreasing solutions for a multi-term fractional-order functional differential equations. We consider Cauchy boundary problems with: nonlocal conditions, two-point boundary conditions, integral conditions, and deviated arguments.

Integral transform method for solving time fractional systems and fractional heat equation

Directory of Open Access Journals (Sweden)

Arman Aghili

2014-01-01

Full Text Available In the present paper, time fractional partial differential equation is considered, where the fractional derivative is defined in the Caputo sense. Laplace transform method has been applied to obtain an exact solution. The authors solved certain homogeneous and nonhomogeneous time fractional heat equations using integral transform. Transform method is a powerful tool for solving fractional singular Integro - differential equations and PDEs. The result reveals that the transform method is very convenient and effective.

The Use of Generalized Laguerre Polynomials in Spectral Methods for Solving Fractional Delay Differential Equations.

Science.gov (United States)

Khader, M M

2013-10-01

In this paper, an efficient numerical method for solving the fractional delay differential equations (FDDEs) is considered. The fractional derivative is described in the Caputo sense. The proposed method is based on the derived approximate formula of the Laguerre polynomials. The properties of Laguerre polynomials are utilized to reduce FDDEs to a linear or nonlinear system of algebraic equations. Special attention is given to study the error and the convergence analysis of the proposed method. Several numerical examples are provided to confirm that the proposed method is in excellent agreement with the exact solution.

Ground State Solutions for a Class of Fractional Differential Equations with Dirichlet Boundary Value Condition

Directory of Open Access Journals (Sweden)

Zhigang Hu

2014-01-01

Full Text Available In this paper, we apply the method of the Nehari manifold to study the fractional differential equation (d/dt((1/2 0Dt-β(u′(t+(1/2 tDT-β(u′(t=  f(t,u(t, a.e. t∈[0,T], and u0=uT=0, where  0Dt-β, tDT-β are the left and right Riemann-Liouville fractional integrals of order 0≤β<1, respectively. We prove the existence of a ground state solution of the boundary value problem.

Fractionation of Pb and Cu in the fine fraction (landfill.

Science.gov (United States)

Kaczala, Fabio; Orupõld, Kaja; Augustsson, Anna; Burlakovs, Juris; Hogland, Marika; Bhatnagar, Amit; Hogland, William

2017-11-01

The fractionation of metals in the fine fraction (landfill was carried out to evaluate the metal (Pb and Cu) contents and their potential towards not only mobility but also possibilities of recovery/extraction. The fractionation followed the BCR (Community Bureau of Reference) sequential extraction, and the exchangeable (F1), reducible (F2), oxidizable (F3) and residual fractions were determined. The results showed that Pb was highly associated with the reducible (F2) and oxidizable (F3) fractions, suggesting the potential mobility of this metal mainly when in contact with oxygen, despite the low association with the exchangeable fraction (F1). Cu has also shown the potential for mobility when in contact with oxygen, since high associations with the oxidizable fraction (F3) were observed. On the other hand, the mobility of metals in excavated waste can be seen as beneficial considering the circular economy and recovery of such valuables back into the economy. To conclude, not only the total concentration of metals but also a better understanding of fractionation and in which form metals are bound is very important to bring information on how to manage the fine fraction from excavated waste both in terms of environmental impacts and also recovery of such valuables in the economy.

Rational fraction application for continuation of differential cross sections of nuclear reactions into the nonphysical region

International Nuclear Information System (INIS)

Borbely, I.; Nichitiu, F.

1975-01-01

We propose to apply rational fraction approximations instead of polynomial ones for analytic continuation of the differential cross section. On the example of p-d scattering it is demonstrated that the spectroscopic in-formation extracted in this way is more reliable

Sequential fractionation and differences in binding forms of risk elements in spinach biomass

Czech Academy of Sciences Publication Activity Database

Pavlíková, D.; Pavlík, Milan; Vašíčková, Soňa; Száková, J.; Tlustoš, P.; Balík, J.

2005-01-01

Roč. 12, 1/2 (2005), s. 101-108 ISSN 1231-7098 R&D Projects: GA MZe(CZ) QF4063 Institutional research plan: CEZ:AV0Z40550506 Keywords : sequential extraction * spinach * risk elements Subject RIV: CC - Organic Chemistry

Fractional gradient and its application to the fractional advection equation

OpenAIRE

D'Ovidio, M.; Garra, R.

2013-01-01

In this paper we provide a definition of fractional gradient operators, related to directional derivatives. We develop a fractional vector calculus, providing a probabilistic interpretation and mathematical tools to treat multidimensional fractional differential equations. A first application is discussed in relation to the d-dimensional fractional advection-dispersion equation. We also study the connection with multidimensional L\\'evy processes.

Sequential Elution of Essential Oil Constituents during Steam Distillation of Hops (Humulus lupulus L.) and Influence on Oil Yield and Antimicrobial Activity.

Science.gov (United States)

Jeliazkova, Ekaterina; Zheljazkov, Valtcho D; Kačániova, Miroslava; Astatkie, Tess; Tekwani, Babu L

2018-06-07

The profile and bioactivity of hops (Humulus lupulus L.) essential oil, a complex natural product extracted from cones via steam distillation, depends on genetic and environmental factors, and may also depend on extraction process. We hypothesized that compound mixtures eluted sequentially and captured at different timeframes during the steam distillation process of whole hop cones would have differential chemical and bioactivity profiles. The essential oil was collected sequentially at 8 distillation time (DT) intervals: 0-2, 2-5, 5-10, 10-30, 30-60, 60-120, 120-180, and 180-240 min. The control was a 4-h non-interrupted distillation. Nonlinear regression models described the DT and essential oil compounds relationship. Fractions yielded 0.035 to 0.313% essential oil, while control yielded 1.47%. The oil eluted during the first hour was 83.2%, 9.6% during the second hour, and only 7.2% during the second half of the distillation. Essential oil (EO) fractions had different chemical profile. Monoterpenes were eluted early, while sequiterpenes were eluted late. Myrcene and linalool were the highest in 0-2 min fraction, β-caryophyllene, β-copaene, β-farnesene, and α-humulene were highest in fractions from middle of distillation, whereas α- bergamotene, γ-muurolene, β- and α-selinene, γ- and δ-cadinene, caryophyllene oxide, humulne epoxide II, τ-cadinol, and 6-pentadecen-2-one were highest in 120-180 or 180-240 min fractions. The Gram-negative Escherichia coli was strongly inhibited by essential oil fractions from 2-5 min and 10-30 min, followed by oil fraction from 0-2 min. The strongest inhibition activity against Gram-negative Yersinia enterocolitica, and Gram-positive Clostridium perfringens, Enterococcus faecalis, and Staphylococcus aureus subs. aureus was observed with the control essential oil. This is the first study to describe significant activity of hops essential oils against Trypanosoma brucei, a parasitic protozoan that causes African

Measurement of the differential branching fraction of the decay Λ{sub b}{sup 0}→Λμ{sup +}μ{sup −}

Energy Technology Data Exchange (ETDEWEB)

Aaij, R. [Nikhef National Institute for Subatomic Physics, Amsterdam (Netherlands); Adeva, B. [Universidad de Santiago de Compostela, Santiago de Compostela (Spain); Adinolfi, M. [H.H. Wills Physics Laboratory, University of Bristol, Bristol (United Kingdom); Adrover, C. [CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille (France); Affolder, A. [Oliver Lodge Laboratory, University of Liverpool, Liverpool (United Kingdom); Ajaltouni, Z. [Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-Ferrand (France); Albrecht, J. [Fakultät Physik, Technische Universität Dortmund, Dortmund (Germany); Alessio, F. [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Alexander, M. [School of Physics and Astronomy, University of Glasgow, Glasgow (United Kingdom); Ali, S. [Nikhef National Institute for Subatomic Physics, Amsterdam (Netherlands); Alkhazov, G. [Petersburg Nuclear Physics Institute (PNPI), Gatchina (Russian Federation); Alvarez Cartelle, P. [Universidad de Santiago de Compostela, Santiago de Compostela (Spain); Alves, A.A. [Sezione INFN di Roma La Sapienza, Roma (Italy); European Organization for Nuclear Research (CERN), Geneva (Switzerland); Amato, S. [Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro (Brazil); Amerio, S. [Sezione INFN di Padova, Padova (Italy); Amhis, Y. [LAL, Université Paris-Sud, CNRS/IN2P3, Orsay (France); Anderlini, L. [Sezione INFN di Firenze, Firenze (Italy); Anderson, J. [Physik-Institut, Universität Zürich, Zürich (Switzerland); Andreassen, R. [University of Cincinnati, Cincinnati, OH (United States); Andrews, J.E. [University of Maryland, College Park, MD (United States); and others

2013-08-09

The differential branching fraction of the decay Λ{sub b}{sup 0}→Λμ{sup +}μ{sup −} is measured as a function of the square of the dimuon invariant mass, q{sup 2}. A yield of 78±12Λ{sub b}{sup 0}→Λμ{sup +}μ{sup −} decays is observed using data, corresponding to an integrated luminosity of 1.0 fb{sup −1}, collected by the LHCb experiment at a centre-of-mass energy of 7 TeV. A significant signal is found in the q{sup 2} region above the square of the J/ψ mass, while at lower-q{sup 2} values upper limits are set on the differential branching fraction. Integrating the differential branching fraction over q{sup 2}, while excluding the J/ψ and ψ(2S) regions, gives a branching fraction of B(Λ{sub b}{sup 0}→Λμ{sup +}μ{sup −})=(0.96±0.16(stat)±0.13(syst)±0.21(norm))×10{sup −6}, where the uncertainties are statistical, systematic and due to the normalisation mode, Λ{sub b}{sup 0}→J/ψΛ, respectively.

Measurements of the S-wave fraction in $B^{0}\\rightarrow K^{+}\\pi^{-}\\mu^{+}\\mu^{-}$ decays and the $B^{0}\\rightarrow K^{\\ast}(892)^{0}\\mu^{+}\\mu^{-}$ differential branching fraction

CERN Document Server

Aaij, Roel; Adinolfi, Marco; Ajaltouni, Ziad; Akar, Simon; Albrecht, Johannes; Alessio, Federico; Alexander, Michael; Ali, Suvayu; Alkhazov, Georgy; Alvarez Cartelle, Paula; Alves Jr, Antonio Augusto; Amato, Sandra; Amerio, Silvia; Amhis, Yasmine; An, Liupan; Anderlini, Lucio; Andreassi, Guido; Andreotti, Mirco; Andrews, Jason; Appleby, Robert; Aquines Gutierrez, Osvaldo; Archilli, Flavio; d'Argent, Philippe; Artamonov, Alexander; Artuso, Marina; Aslanides, Elie; Auriemma, Giulio; Baalouch, Marouen; Bachmann, Sebastian; Back, John; Badalov, Alexey; Baesso, Clarissa; Baldini, Wander; Barlow, Roger; Barschel, Colin; Barsuk, Sergey; Barter, William; Batozskaya, Varvara; Battista, Vincenzo; Bay, Aurelio; Beaucourt, Leo; Beddow, John; Bedeschi, Franco; Bediaga, Ignacio; Bel, Lennaert; Bellee, Violaine; Belloli, Nicoletta; Belous, Konstantin; Belyaev, Ivan; Ben-Haim, Eli; Bencivenni, Giovanni; Benson, Sean; Benton, Jack; Berezhnoy, Alexander; Bernet, Roland; Bertolin, Alessandro; Bettler, Marc-Olivier; van Beuzekom, Martinus; Bifani, Simone; Billoir, Pierre; Bird, Thomas; Birnkraut, Alex; Bitadze, Alexander; Bizzeti, Andrea; Blake, Thomas; Blanc, Frederic; Blouw, Johan; Blusk, Steven; Bocci, Valerio; Boettcher, Thomas; Bondar, Alexander; Bondar, Nikolay; Bonivento, Walter; Borghi, Silvia; Borisyak, Maxim; Borsato, Martino; Bossu, Francesco; Boubdir, Meriem; Bowcock, Themistocles; Bowen, Espen Eie; Bozzi, Concezio; Braun, Svende; Britsch, Markward; Britton, Thomas; Brodzicka, Jolanta; Buchanan, Emma; Burr, Christopher; Bursche, Albert; Buytaert, Jan; Cadeddu, Sandro; Calabrese, Roberto; Calvi, Marta; Calvo Gomez, Miriam; Campana, Pierluigi; Campora Perez, Daniel; Capriotti, Lorenzo; Carbone, Angelo; Carboni, Giovanni; Cardinale, Roberta; Cardini, Alessandro; Carniti, Paolo; Carson, Laurence; Carvalho Akiba, Kazuyoshi; Casse, Gianluigi; Cassina, Lorenzo; Castillo Garcia, Lucia; Cattaneo, Marco; Cauet, Christophe; Cavallero, Giovanni; Cenci, Riccardo; Charles, Matthew; Charpentier, Philippe; Chatzikonstantinidis, Georgios; Chefdeville, Maximilien; Chen, Shanzhen; Cheung, Shu-Faye; Chobanova, Veronika; Chrzaszcz, Marcin; Cid Vidal, Xabier; Ciezarek, Gregory; Clarke, Peter; Clemencic, Marco; Cliff, Harry; Closier, Joel; Coco, Victor; Cogan, Julien; Cogneras, Eric; Cogoni, Violetta; Cojocariu, Lucian; Collazuol, Gianmaria; Collins, Paula; Comerma-Montells, Albert; Contu, Andrea; Cook, Andrew; Coquereau, Samuel; Corti, Gloria; Corvo, Marco; Couturier, Benjamin; Cowan, Greig; Craik, Daniel Charles; Crocombe, Andrew; Cruz Torres, Melissa Maria; Cunliffe, Samuel; Currie, Robert; D'Ambrosio, Carmelo; Dall'Occo, Elena; Dalseno, Jeremy; David, Pieter; Davis, Adam; De Aguiar Francisco, Oscar; De Bruyn, Kristof; De Capua, Stefano; De Cian, Michel; De Miranda, Jussara; De Paula, Leandro; De Simone, Patrizia; Dean, Cameron Thomas; Decamp, Daniel; Deckenhoff, Mirko; Del Buono, Luigi; Demmer, Moritz; Derkach, Denis; Deschamps, Olivier; Dettori, Francesco; Dey, Biplab; Di Canto, Angelo; Dijkstra, Hans; Dordei, Francesca; Dorigo, Mirco; Dosil Suárez, Alvaro; Dovbnya, Anatoliy; Dreimanis, Karlis; Dufour, Laurent; Dujany, Giulio; Dungs, Kevin; Durante, Paolo; Dzhelyadin, Rustem; Dziurda, Agnieszka; Dzyuba, Alexey; Déléage, Nicolas; Easo, Sajan; Egede, Ulrik; Egorychev, Victor; Eidelman, Semen; Eisenhardt, Stephan; Eitschberger, Ulrich; Ekelhof, Robert; Eklund, Lars; Elsasser, Christian; Ely, Scott; Esen, Sevda; Evans, Hannah Mary; Evans, Timothy; Falabella, Antonio; Farley, Nathanael; Farry, Stephen; Fay, Robert; Ferguson, Dianne; Fernandez Albor, Victor; Ferrari, Fabio; Ferreira Rodrigues, Fernando; Ferro-Luzzi, Massimiliano; Filippov, Sergey; Fiore, Marco; Fiorini, Massimiliano; Firlej, Miroslaw; Fitzpatrick, Conor; Fiutowski, Tomasz; Fleuret, Frederic; Fohl, Klaus; Fontana, Marianna; Fontanelli, Flavio; Forshaw, Dean Charles; Forty, Roger; Frank, Markus; Frei, Christoph; Frosini, Maddalena; Fu, Jinlin; Furfaro, Emiliano; Färber, Christian; Gallas Torreira, Abraham; Galli, Domenico; Gallorini, Stefano; Gambetta, Silvia; Gandelman, Miriam; Gandini, Paolo; Gao, Yuanning; García Pardiñas, Julián; Garra Tico, Jordi; Garrido, Lluis; Garsed, Philip John; Gascon, David; Gaspar, Clara; Gavardi, Laura; Gazzoni, Giulio; Gerick, David; Gersabeck, Evelina; Gersabeck, Marco; Gershon, Timothy; Ghez, Philippe; Gianì, Sebastiana; Gibson, Valerie; Girard, Olivier Göran; Giubega, Lavinia-Helena; Gizdov, Konstantin; Gligorov, V.V.; Golubkov, Dmitry; Golutvin, Andrey; Gomes, Alvaro; Gorelov, Igor Vladimirovich; Gotti, Claudio; Grabalosa Gándara, Marc; Graciani Diaz, Ricardo; Granado Cardoso, Luis Alberto; Graugés, Eugeni; Graverini, Elena; Graziani, Giacomo; Grecu, Alexandru; Griffith, Peter; Grillo, Lucia; Grünberg, Oliver; Gushchin, Evgeny; Guz, Yury; Gys, Thierry; Göbel, Carla; Hadavizadeh, Thomas; Hadjivasiliou, Christos; Haefeli, Guido; Haen, Christophe; Haines, Susan; Hall, Samuel; Hamilton, Brian; Han, Xiaoxue; Hansmann-Menzemer, Stephanie; Harnew, Neville; Harnew, Samuel; Harrison, Jonathan; He, Jibo; Head, Timothy; Heister, Arno; Hennessy, Karol; Henrard, Pierre; Henry, Louis; Hernando Morata, Jose Angel; van Herwijnen, Eric; Heß, Miriam; Hicheur, Adlène; Hill, Donal; Hombach, Christoph; Hulsbergen, Wouter; Humair, Thibaud; Hushchyn, Mikhail; Hussain, Nazim; Hutchcroft, David; Idzik, Marek; Ilten, Philip; Jacobsson, Richard; Jaeger, Andreas; Jalocha, Pawel; Jans, Eddy; Jawahery, Abolhassan; John, Malcolm; Johnson, Daniel; Jones, Christopher; Joram, Christian; Jost, Beat; Jurik, Nathan; Kandybei, Sergii; Kanso, Walaa; Karacson, Matthias; Karbach, Moritz; Karodia, Sarah; Kecke, Matthieu; Kelsey, Matthew; Kenyon, Ian; Kenzie, Matthew; Ketel, Tjeerd; Khairullin, Egor; Khanji, Basem; Khurewathanakul, Chitsanu; Kirn, Thomas; Klaver, Suzanne; Klimaszewski, Konrad; Kolpin, Michael; Komarov, Ilya; Koopman, Rose; Koppenburg, Patrick; Kozachuk, Anastasiia; Kozeiha, Mohamad; Kravchuk, Leonid; Kreplin, Katharina; Kreps, Michal; Krokovny, Pavel; Kruse, Florian; Krzemien, Wojciech; Kucewicz, Wojciech; Kucharczyk, Marcin; Kudryavtsev, Vasily; Kuonen, Axel Kevin; Kurek, Krzysztof; Kvaratskheliya, Tengiz; Lacarrere, Daniel; Lafferty, George; Lai, Adriano; Lambert, Dean; Lanfranchi, Gaia; Langenbruch, Christoph; Langhans, Benedikt; Latham, Thomas; Lazzeroni, Cristina; Le Gac, Renaud; van Leerdam, Jeroen; Lees, Jean-Pierre; Leflat, Alexander; Lefrançois, Jacques; Lefèvre, Regis; Lemaitre, Florian; Lemos Cid, Edgar; Leroy, Olivier; Lesiak, Tadeusz; Leverington, Blake; Li, Yiming; Likhomanenko, Tatiana; Lindner, Rolf; Linn, Christian; Lionetto, Federica; Liu, Bo; Liu, Xuesong; Loh, David; Longstaff, Iain; Lopes, Jose; Lucchesi, Donatella; Lucio Martinez, Miriam; Luo, Haofei; Lupato, Anna; Luppi, Eleonora; Lupton, Oliver; Lusiani, Alberto; Lyu, Xiao-Rui; Machefert, Frederic; Maciuc, Florin; Maev, Oleg; Maguire, Kevin; Malde, Sneha; Malinin, Alexander; Maltsev, Timofei; Manca, Giulia; Mancinelli, Giampiero; Manning, Peter Michael; Maratas, Jan; Marchand, Jean François; Marconi, Umberto; Marin Benito, Carla; Marino, Pietro; Marks, Jörg; Martellotti, Giuseppe; Martin, Morgan; Martinelli, Maurizio; Martinez Santos, Diego; Martinez Vidal, Fernando; Martins Tostes, Danielle; Massacrier, Laure Marie; Massafferri, André; Matev, Rosen; Mathad, Abhijit; Mathe, Zoltan; Matteuzzi, Clara; Mauri, Andrea; Maurin, Brice; Mazurov, Alexander; McCann, Michael; McCarthy, James; McNab, Andrew; McNulty, Ronan; Meadows, Brian; Meier, Frank; Meissner, Marco; Melnychuk, Dmytro; Merk, Marcel; Michielin, Emanuele; Milanes, Diego Alejandro; Minard, Marie-Noelle; Mitzel, Dominik Stefan; Molina Rodriguez, Josue; Monroy, Ignacio Alberto; Monteil, Stephane; Morandin, Mauro; Morawski, Piotr; Mordà, Alessandro; Morello, Michael Joseph; Moron, Jakub; Morris, Adam Benjamin; Mountain, Raymond; Muheim, Franz; Mulder, Mick; Mussini, Manuel; Müller, Dominik; Müller, Janine; Müller, Katharina; Müller, Vanessa; Naik, Paras; Nakada, Tatsuya; Nandakumar, Raja; Nandi, Anita; Nasteva, Irina; Needham, Matthew; Neri, Nicola; Neubert, Sebastian; Neufeld, Niko; Neuner, Max; Nguyen, Anh Duc; Nguyen-Mau, Chung; Niess, Valentin; Nieswand, Simon; Niet, Ramon; Nikitin, Nikolay; Nikodem, Thomas; Novoselov, Alexey; O'Hanlon, Daniel Patrick; Oblakowska-Mucha, Agnieszka; Obraztsov, Vladimir; Ogilvy, Stephen; Oldeman, Rudolf; Onderwater, Gerco; Otalora Goicochea, Juan Martin; Otto, Adam; Owen, Patrick; Oyanguren, Maria Aranzazu; Palano, Antimo; Palombo, Fernando; Palutan, Matteo; Panman, Jacob; Papanestis, Antonios; Pappagallo, Marco; Pappalardo, Luciano; Pappenheimer, Cheryl; Parker, William; Parkes, Christopher; Passaleva, Giovanni; Patel, Girish; Patel, Mitesh; Patrignani, Claudia; Pearce, Alex; Pellegrino, Antonio; Penso, Gianni; Pepe Altarelli, Monica; Perazzini, Stefano; Perret, Pascal; Pescatore, Luca; Petridis, Konstantinos; Petrolini, Alessandro; Petrov, Aleksandr; Petruzzo, Marco; Picatoste Olloqui, Eduardo; Pietrzyk, Boleslaw; Pikies, Malgorzata; Pinci, Davide; Pistone, Alessandro; Piucci, Alessio; Playfer, Stephen; Plo Casasus, Maximo; Poikela, Tuomas; Polci, Francesco; Poluektov, Anton; Polyakov, Ivan; Polycarpo, Erica; Pomery, Gabriela Johanna; Popov, Alexander; Popov, Dmitry; Popovici, Bogdan; Potterat, Cédric; Price, Eugenia; Price, Joseph David; Prisciandaro, Jessica; Pritchard, Adrian; Prouve, Claire; Pugatch, Valery; Puig Navarro, Albert; Punzi, Giovanni; Qian, Wenbin; Quagliani, Renato; Rachwal, Bartolomiej; Rademacker, Jonas; Rama, Matteo; Ramos Pernas, Miguel; Rangel, Murilo; Raniuk, Iurii; Raven, Gerhard; Redi, Federico; Reichert, Stefanie; dos Reis, Alberto; Remon Alepuz, Clara; Renaudin, Victor; Ricciardi, Stefania; Richards, Sophie; Rihl, Mariana; Rinnert, Kurt; Rives Molina, Vicente; Robbe, Patrick; Rodrigues, Ana Barbara; Rodrigues, Eduardo; Rodriguez Lopez, Jairo Alexis; Rodriguez Perez, Pablo; Rogozhnikov, Alexey; Roiser, Stefan; Romanovskiy, Vladimir; Romero Vidal, Antonio; Ronayne, John William; Rotondo, Marcello; Ruf, Thomas; Ruiz Valls, Pablo; Saborido Silva, Juan Jose; Sagidova, Naylya; Saitta, Biagio; Salustino Guimaraes, Valdir; Sanchez Mayordomo, Carlos; Sanmartin Sedes, Brais; Santacesaria, Roberta; Santamarina Rios, Cibran; Santimaria, Marco; Santovetti, Emanuele; Sarti, Alessio; Satriano, Celestina; Satta, Alessia; Saunders, Daniel Martin; Savrina, Darya; Schael, Stefan; Schellenberg, Margarete; Schiller, Manuel; Schindler, Heinrich; Schlupp, Maximilian; Schmelling, Michael; Schmelzer, Timon; Schmidt, Burkhard; Schneider, Olivier; Schopper, Andreas; Schubert, Konstantin; Schubiger, Maxime; Schune, Marie Helene; Schwemmer, Rainer; Sciascia, Barbara; Sciubba, Adalberto; Semennikov, Alexander; Sergi, Antonino; Serra, Nicola; Serrano, Justine; Sestini, Lorenzo; Seyfert, Paul; Shapkin, Mikhail; Shapoval, Illya; Shcheglov, Yury; Shears, Tara; Shekhtman, Lev; Shevchenko, Vladimir; Shires, Alexander; Siddi, Benedetto Gianluca; Silva Coutinho, Rafael; Silva de Oliveira, Luiz Gustavo; Simi, Gabriele; Sirendi, Marek; Skidmore, Nicola; Skwarnicki, Tomasz; Smith, Eluned; Smith, Iwan Thomas; Smith, Jackson; Smith, Mark; Snoek, Hella; Sokoloff, Michael; Soler, Paul; Souza, Daniel; Souza De Paula, Bruno; Spaan, Bernhard; Spradlin, Patrick; Sridharan, Srikanth; Stagni, Federico; Stahl, Marian; Stahl, Sascha; Stefko, Pavol; Stefkova, Slavorima; Steinkamp, Olaf; Stenyakin, Oleg; Stevenson, Scott; Stoica, Sabin; Stone, Sheldon; Storaci, Barbara; Stracka, Simone; Straticiuc, Mihai; Straumann, Ulrich; Sun, Liang; Sutcliffe, William; Swientek, Krzysztof; Syropoulos, Vasileios; Szczekowski, Marek; Szumlak, Tomasz; T'Jampens, Stephane; Tayduganov, Andrey; Tekampe, Tobias; Tellarini, Giulia; Teubert, Frederic; Thomas, Christopher; Thomas, Eric; van Tilburg, Jeroen; Tisserand, Vincent; Tobin, Mark; Tolk, Siim; Tomassetti, Luca; Tonelli, Diego; Topp-Joergensen, Stig; Tournefier, Edwige; Tourneur, Stephane; Trabelsi, Karim; Traill, Murdo; Tran, Minh Tâm; Tresch, Marco; Trisovic, Ana; Tsaregorodtsev, Andrei; Tsopelas, Panagiotis; Tuning, Niels; Ukleja, Artur; Ustyuzhanin, Andrey; Uwer, Ulrich; Vacca, Claudia; Vagnoni, Vincenzo; Valat, Sebastien; Valenti, Giovanni; Vallier, Alexis; Vazquez Gomez, Ricardo; Vazquez Regueiro, Pablo; Vecchi, Stefania; van Veghel, Maarten; Velthuis, Jaap; Veltri, Michele; Veneziano, Giovanni; Venkateswaran, Aravindhan; Vesterinen, Mika; Viaud, Benoit; Vieira, Daniel; Vieites Diaz, Maria; Vilasis-Cardona, Xavier; Volkov, Vladimir; Vollhardt, Achim; Voneki, Balazs; Voong, David; Vorobyev, Alexey; Vorobyev, Vitaly; Voß, Christian; de Vries, Jacco; Vázquez Sierra, Carlos; Waldi, Roland; Wallace, Charlotte; Wallace, Ronan; Walsh, John; Wang, Jianchun; Ward, David; Watson, Nigel; Websdale, David; Weiden, Andreas; Whitehead, Mark; Wicht, Jean; Wilkinson, Guy; Wilkinson, Michael; Williams, Mark Richard James; Williams, Matthew; Williams, Mike; Williams, Timothy; Wilson, Fergus; Wimberley, Jack; Wishahi, Julian; Wislicki, Wojciech; Witek, Mariusz; Wormser, Guy; Wotton, Stephen; Wraight, Kenneth; Wright, Simon; Wyllie, Kenneth; Xie, Yuehong; Xing, Zhou; Xu, Zhirui; Yang, Zhenwei; Yin, Hang; Yu, Jiesheng; Yuan, Xuhao; Yushchenko, Oleg; Zangoli, Maria; Zarebski, Kristian Alexander; Zavertyaev, Mikhail; Zhang, Liming; Zhang, Yanxi; Zhang, Yu; Zhelezov, Alexey; Zheng, Yangheng; Zhokhov, Anatoly; Zhukov, Valery; Zucchelli, Stefano

2016-11-08

A measurement of the differential branching fraction of the decay ${B^{0}\\rightarrow K^{\\ast}(892)^{0}\\mu^{+}\\mu^{-}}$ is presented together with a determination of the S-wave fraction of the $K^+\\pi^-$ system in the decay $B^{0}\\rightarrow K^{+}\\pi^{-}\\mu^{+}\\mu^{-}$. The analysis is based on $pp$-collision data corresponding to an integrated luminosity of 3\\,fb$^{-1}$ collected with the LHCb experiment. The measurements are made in bins of the invariant mass squared of the dimuon system, $q^2$. Precise theoretical predictions for the differential branching fraction of $B^{0}\\rightarrow K^{\\ast}(892)^{0}\\mu^{+}\\mu^{-}$ decays are available for the $q^2$ region $1.1fraction of the $K^+\\pi^-$ system in $B^{0}\\rightarrow K^{+}\\pi^{-}\\mu^{+}\\mu^{-}$ decays is found to be \\begin{equation*} F_{\\rm S} = 0.101\\pm0.017({\\rm stat})\\pm0.009 ({\\rm syst}), \\end{equation*}...

Differential branching fraction and angular analysis of the decay B-0 -> K*(0)mu(+)mu(-)

NARCIS (Netherlands)

Aaij, R.; Abellan Beteta, C.; Adeva, B.; Adinolfi, M.; Adrover, C.; Affolder, A.; Ajaltouni, Z.; Albrecht, J.; Alessio, F.; Alexander, M.; Ali, S.; Alkhazov, G.; Alvarez Cartelle, P.; Alves, A. A.; Amato, S.; Amerio, S.; Amhis, Y.; Anderlini, L.; Andreassen, R.; Appleby, R. B.; Aquines Gutierrez, O.; Archilli, F.; Artamonov, A.; Artuso, M.; Aslanides, E.; Auriemma, G.; Bachmann, S.; Back, J. J.; Baesso, C.; Balagura, V.; Baldini, W.; Barlow, R. J.; Barschel, C.; Barsuk, S.; Barter, W.; Bauer, Th.; Beddow, J.; Bedeschi, F.; Bediaga, I.; Belogurov, S.; Belous, K.; Belyaev, I.; Ben-Haim, E.; Bencivenni, G.; Benson, S.; Benton, J.; Berezhnoy, A.; Bernet, R.; Pellegrino, A.; Tolk, S.

The angular distribution and differential branching fraction of the decay B-0 -> K*(0)mu(+)mu(-) are studied using a data sample, collected by the LHCb experiment in pp collisions at root s = 7 TeV, corresponding to an integrated luminosity of 1.0 fb(-1). Several angular observables are measured in

A new modification in the exponential rational function method for nonlinear fractional differential equations

Science.gov (United States)

Ahmed, Naveed; Bibi, Sadaf; Khan, Umar; Mohyud-Din, Syed Tauseef

2018-02-01

We have modified the traditional exponential rational function method (ERFM) and have used it to find the exact solutions of two different fractional partial differential equations, one is the time fractional Boussinesq equation and the other is the (2+1)-dimensional time fractional Zoomeron equation. In both the cases it is observed that the modified scheme provides more types of solutions than the traditional one. Moreover, a comparison of the recent solutions is made with some already existing solutions. We can confidently conclude that the modified scheme works better and provides more types of solutions with almost similar computational cost. Our generalized solutions include periodic, soliton-like, singular soliton and kink solutions. A graphical simulation of all types of solutions is provided and the correctness of the solution is verified by direct substitution. The extended version of the solutions is expected to provide more flexibility to scientists working in the relevant field to test their simulation data.

Polarization control of direct (non-sequential) two-photon double ionization of He

International Nuclear Information System (INIS)

Pronin, E A; Manakov, N L; Marmo, S I; Starace, Anthony F

2007-01-01

An ab initio parametrization of the doubly-differential cross section (DDCS) for two-photon double ionization (TPDI) from an s 2 subshell of an atom in a 1 S 0 -state is presented. Analysis of the elliptic dichroism (ED) effect in the DDCS for TPDI of He and its comparison with the same effect in the concurrent process of sequential double ionization shows their qualitative and quantitative differences, thus providing a means to control and to distinguish sequential and non-sequential processes by measuring the relative ED parameter

Existence of positive solutions for boundary value problems of fractional functional differential equations

Directory of Open Access Journals (Sweden)

Chuanzhi Bai

2010-06-01

Full Text Available This paper deals with the existence of positive solutions for a boundary value problem involving a nonlinear functional differential equation of fractional order $\\alpha$ given by $ D^{\\alpha} u(t + f(t, u_t = 0$, $t \\in (0, 1$, $2 < \\alpha \\le 3$, $ u^{\\prime}(0 = 0$, $u^{\\prime}(1 = b u^{\\prime}(\\eta$, $u_0 = \\phi$. Our results are based on the nonlinear alternative of Leray-Schauder type and Krasnosel'skii fixed point theorem.

Generalized Asymptotically Almost Periodic and Generalized Asymptotically Almost Automorphic Solutions of Abstract Multiterm Fractional Differential Inclusions

Directory of Open Access Journals (Sweden)

G. M. N’Guérékata

2018-01-01

Full Text Available The main aim of this paper is to investigate generalized asymptotical almost periodicity and generalized asymptotical almost automorphy of solutions to a class of abstract (semilinear multiterm fractional differential inclusions with Caputo derivatives. We illustrate our abstract results with several examples and possible applications.

Asymptotic integration of some nonlinear differential equations with fractional time derivative

International Nuclear Information System (INIS)

Baleanu, Dumitru; Agarwal, Ravi P; Mustafa, Octavian G; Cosulschi, Mirel

2011-01-01

We establish that, under some simple integral conditions regarding the nonlinearity, the (1 + α)-order fractional differential equation 0 D α t (x') + f(t, x) = 0, t > 0, has a solution x element of C([0,+∞),R) intersection C 1 ((0,+∞),R), with lim t→0 [t 1-α x'(t)] element of R, which can be expanded asymptotically as a + bt α + O(t α-1 ) when t → +∞ for given real numbers a, b. Our arguments are based on fixed point theory. Here, 0 D α t designates the Riemann-Liouville derivative of order α in (0, 1).

Modulating Functions Based Algorithm for the Estimation of the Coefficients and Differentiation Order for a Space-Fractional Advection-Dispersion Equation

KAUST Repository

Aldoghaither, Abeer

2015-12-01

In this paper, a new method, based on the so-called modulating functions, is proposed to estimate average velocity, dispersion coefficient, and differentiation order in a space-fractional advection-dispersion equation, where the average velocity and the dispersion coefficient are space-varying. First, the average velocity and the dispersion coefficient are estimated by applying the modulating functions method, where the problem is transformed into a linear system of algebraic equations. Then, the modulating functions method combined with a Newton\\'s iteration algorithm is applied to estimate the coefficients and the differentiation order simultaneously. The local convergence of the proposed method is proved. Numerical results are presented with noisy measurements to show the effectiveness and robustness of the proposed method. It is worth mentioning that this method can be extended to general fractional partial differential equations.

Modulating Functions Based Algorithm for the Estimation of the Coefficients and Differentiation Order for a Space-Fractional Advection-Dispersion Equation

KAUST Repository

Aldoghaither, Abeer; Liu, Da-Yan; Laleg-Kirati, Taous-Meriem

2015-01-01

In this paper, a new method, based on the so-called modulating functions, is proposed to estimate average velocity, dispersion coefficient, and differentiation order in a space-fractional advection-dispersion equation, where the average velocity and the dispersion coefficient are space-varying. First, the average velocity and the dispersion coefficient are estimated by applying the modulating functions method, where the problem is transformed into a linear system of algebraic equations. Then, the modulating functions method combined with a Newton's iteration algorithm is applied to estimate the coefficients and the differentiation order simultaneously. The local convergence of the proposed method is proved. Numerical results are presented with noisy measurements to show the effectiveness and robustness of the proposed method. It is worth mentioning that this method can be extended to general fractional partial differential equations.

HL-60 differentiating activity and flavonoid content of the readily extractable fraction prepared from citrus juices.

Science.gov (United States)

Kawaii, S; Tomono, Y; Katase, E; Ogawa, K; Yano, M

1999-01-01

Citrus plants are rich sources of various bioactive flavonoids. To eliminate masking effects caused by hesperidin, naringin, and neoeriocitrin, the abundant flavonoid glycosides which make up 90% of the conventionally prepared sample, the readily extractable fraction from Citrus juice was prepared by adsorbing on HP-20 resin and eluting with EtOH and acetone from the resin and was subjected to HL-60 differentiation assay and quantitative analysis of major flavonoids. Screening of 34 Citrus juices indicated that King (C. nobilis) had a potent activity for inducing differentiation of HL-60, and the active principles were isolated and identified as four polymethoxylated flavonoids, namely, nobiletin, 3,3',4',5,6,7, 8-heptamethoxyflavone, natsudaidain, and tangeretin. HPLC analysis of the readily extractable fraction also indicated that King contained high amounts of these polymethoxylated flavonoids among the Citrus juices examined. Principal component and cluster analyses of the readily extractable flavonoids indicated peculiarities of King and Bergamot.

Chromatin plasticity as a differentiation index during muscle differentiation of C2C12 myoblasts

International Nuclear Information System (INIS)

Watanabe, Tomonobu M.; Higuchi, Sayaka; Kawauchi, Keiko; Tsukasaki, Yoshikazu; Ichimura, Taro; Fujita, Hideaki

2012-01-01

Highlights: ► Change in the epigenetic landscape during myogenesis was optically investigated. ► Mobility of nuclear proteins was used to state the epigenetic status of the cell. ► Mobility of nuclear proteins decreased as myogenesis progressed in C2C12. ► Differentiation state diagram was developed using parameters obtained. -- Abstract: Skeletal muscle undergoes complicated differentiation steps that include cell-cycle arrest, cell fusion, and maturation, which are controlled through sequential expression of transcription factors. During muscle differentiation, remodeling of the epigenetic landscape is also known to take place on a large scale, determining cell fate. In an attempt to determine the extent of epigenetic remodeling during muscle differentiation, we characterized the plasticity of the chromatin structure using C2C12 myoblasts. Differentiation of C2C12 cells was induced by lowering the serum concentration after they had reached full confluence, resulting in the formation of multi-nucleated myotubes. Upon induction of differentiation, the nucleus size decreased whereas the aspect ratio increased, indicating the presence of force on the nucleus during differentiation. Movement of the nucleus was also suppressed when differentiation was induced, indicating that the plasticity of chromatin changed upon differentiation. To evaluate the histone dynamics during differentiation, FRAP experiment was performed, which showed an increase in the immobile fraction of histone proteins when differentiation was induced. To further evaluate the change in the histone dynamics during differentiation, FCS was performed, which showed a decrease in histone mobility on differentiation. We here show that the plasticity of chromatin decreases upon differentiation, which takes place in a stepwise manner, and that it can be used as an index for the differentiation stage during myogenesis using the state diagram developed with the parameters obtained in this study.

Estimation of environmental mobility of heavy metals using a sequential leaching of particulate material emitted from an opencast chrome mine complex

Energy Technology Data Exchange (ETDEWEB)

Poeykioe, R. [Meri-Lappi Institute, Centre for Environmental Technology, University of Oulu, Kemi (Finland); Peraemaeki, P.; Kuokkanen, T. [University of Oulu, Department of Chemistry, Oulu (Finland); Vaelimaeki, I. [Suomen Ympaeristoepalvelu Oy, Oulu (Finland)

2002-06-01

A four-stage sequential leaching procedure was applied to assess the bioavailability and environmental mobility of heavy metals (Cr, Fe, Cu, Ni and Cd) in total suspended particulate (TSP) material emitted from an opencast chrome mine complex (Kemi, Northern Finland). TSP material was collected on glass fibre filters by a high-volume sampler, and a sequential leaching procedure was used to determine the distribution of heavy metals between the water-soluble fraction (H{sub 2}O), environmentally mobile fraction (CH{sub 3}COONH{sub 4}), the fraction bound to carbonate and oxides (HONH{sub 3}Cl + CH{sub 3}COOH), and the fraction bound to silicates and organic matter, that is the environmentally immobile fraction (HNO{sub 3} + HF + HCl). The sequential leaching procedure was also applied to the certified reference materials VKI (QC Loam Soil A) and PACS-2 (Marine Sediment) to evaluate the accuracy and reproducibility of the leaching procedure. The heavy metals were determined by graphite furnace atomic absorption spectrometry (GFAAS) and flame atomic absorption spectrometry (FAAS). The concentrations of metals in the water-soluble fraction (H{sub 2}O) decreased in the order Fe >Cu >Cr >Ni >Cd, and in the environmentally mobile fraction (CH{sub 3}COONH{sub 4}) in the order Cu >Fe >Ni >Cr >Cd. (orig.)

Fractional Dynamics and Control

CERN Document Server

Machado, José; Luo, Albert

2012-01-01

Fractional Dynamics and Control provides a comprehensive overview of recent advances in the areas of nonlinear dynamics, vibration and control with analytical, numerical, and experimental results. This book provides an overview of recent discoveries in fractional control, delves into fractional variational principles and differential equations, and applies advanced techniques in fractional calculus to solving complicated mathematical and physical problems.Finally, this book also discusses the role that fractional order modeling can play in complex systems for engineering and science. Discusses how fractional dynamics and control can be used to solve nonlinear science and complexity issues Shows how fractional differential equations and models can be used to solve turbulence and wave equations in mechanics and gravity theories and Schrodinger’s equation  Presents factional relaxation modeling of dielectric materials and wave equations for dielectrics  Develops new methods for control and synchronization of...

Magma differentiation fractionates Mo isotope ratios: Evidence from the Kos Plateau Tuff (Aegean Arc)

Science.gov (United States)

Voegelin, Andrea R.; Pettke, Thomas; Greber, Nicolas D.; von Niederhäusern, Brigitte; Nägler, Thomas F.

2014-03-01

We investigated high temperature Mo isotope fractionation in a hydrous supra-subduction volcano-plutonic system (Kos, Aegean Arc, Greece) in order to address the debate on the δ98/95Mo variability of the continental crust. In this igneous system, where differentiation is interpreted to be dominated by fractional crystallization, bulk rock data from olivine basalt to dacite show δ98/95Mo ratios increasing from + 0.3 to + 0.6‰ along with Mo concentrations increasing from 0.8 to 4.1 μg g- 1. Data for hornblende and biotite mineral separates reveal the extraction of light Mo into crystallizing silicates, with minimum partition coefficients between hornblende-silicate melt and biotite-silicate melt of 0.6 and 0.4 δ98/95Mo, respectively.

Usefulness of the troponin-ejection fraction product to differentiate stress cardiomyopathy from ST-segment elevation myocardial infarction.

Science.gov (United States)

Nascimento, Francisco O; Yang, Solomon; Larrauri-Reyes, Maiteder; Pineda, Andres M; Cornielle, Vertilio; Santana, Orlando; Heimowitz, Todd B; Stone, Gregg W; Beohar, Nirat

2014-02-01

The presentation of stress cardiomyopathy (SC) with nonobstructive coronary artery disease mimics that of ST-segment elevation myocardial infarction (STEMI) due to coronary occlusion. No single parameter has been successful in differentiating the 2 entities. We thus sought to develop a noninvasive clinical tool to discriminate between these 2 conditions. We retrospectively reviewed 59 consecutive cases of SC at our institution from July 2005 through June 2011 and compared those with 60 consecutives cases of angiographically confirmed STEMI treated with primary percutaneous coronary intervention in the same period. All patients underwent acute echocardiography, and the peak troponin I level was determined. The troponin-ejection fraction product (TEFP) was derived by multiplying the peak troponin I level and the echocardiographically derived left ventricular ejection fraction. Comparing the SC and STEMI groups, the mean left ventricular ejection fraction at the time of presentation was 30 ± 9% versus 44 ± 11%, respectively (p statistic 0.91 ± 0.02, p <0.001). In conclusion, for patients not undergoing emergent angiography, the TEFP may be used with high accuracy to differentiate SC with nonobstructive coronary artery disease from true STEMI due to coronary occlusion. Copyright © 2014 Elsevier Inc. All rights reserved.

Manganese Fractionation Using a Sequential Extraction Method to Evaluate Welders' Shielded Metal Arc Welding Exposures During Construction Projects in Oil Refineries.

Science.gov (United States)

Hanley, Kevin W; Andrews, Ronnee; Bertke, Steven; Ashley, Kevin

2015-01-01

The National Institute for Occupational Safety and Health has conducted an occupational exposure assessment study of manganese (Mn) in welding fume of construction workers rebuilding tanks, piping, and process equipment at two oil refineries. The objective of this study was to evaluate exposures to different Mn fractions using a sequential extraction procedure. Seventy-two worker-days were monitored for either total or respirable Mn during stick welding and associated activities both within and outside of confined spaces. The samples were analyzed using an experimental method to separate different Mn fractions by valence states based on selective chemical solubility. The full-shift total particulate Mn time-weighted average (TWA) breathing zone concentrations ranged from 0.013-29 for soluble Mn in a mild ammonium acetate solution; from 0.26-250 for Mn(0,2+) in acetic acid; from non-detectable (ND) - 350 for Mn(3+,4+) in hydroxylamine-hydrochloride; and from ND - 39 micrograms per cubic meter (μg/m(3)) for insoluble Mn fractions in hydrochloric and nitric acid. The summation of all Mn fractions in total particulate TWA ranged from 0.52-470 μg/m(3). The range of respirable particulate Mn TWA concentrations were from 0.20-28 for soluble Mn; from 1.4-270 for Mn(0,2+); from 0.49-150 for Mn(3+,4+); from ND - 100 for insoluble Mn; and from 2.0-490 μg/m(3) for Mn (sum of fractions). For all jobs combined, total particulate TWA GM concentrations of the Mn(sum) were 99 (GSD = 3.35) and 8.7 (GSD = 3.54) μg/m(3) for workers inside and outside of confined spaces; respirable Mn also showed much higher levels for welders within confined spaces. Regardless of particle size and confined space work status, Mn(0,2+) fraction was the most abundant followed by Mn(3+,4+) fraction, typically >50% and ∼30-40% of Mn(sum), respectively. Eighteen welders' exposures exceeded the ACGIH Threshold Limit Values for total Mn (100 μg/m(3)) and 25 exceeded the recently adopted respirable

A Numerical Algorithm for Solving a Four-Point Nonlinear Fractional Integro-Differential Equations

OpenAIRE

Gao, Er; Song, Songhe; Zhang, Xinjian

2012-01-01

We provide a new algorithm for a four-point nonlocal boundary value problem of nonlinear integro-differential equations of fractional order q∈(1,2] based on reproducing kernel space method. According to our work, the analytical solution of the equations is represented in the reproducing kernel space which we construct and so the n-term approximation. At the same time, the n-term approximation is proved to converge to the analytical solution. An illustrative example is also presented, which sh...

Mass dependent fractionation of stable chromium isotopes in mare basalts: Implications for the formation and the differentiation of the Moon

Science.gov (United States)

Bonnand, Pierre; Parkinson, Ian J.; Anand, Mahesh

2016-02-01

We present the first stable chromium isotopic data from mare basalts in order to investigate the similarity between the Moon and the Earth's mantle. A double spike technique coupled with MC-ICP-MS measurements was used to analyse 19 mare basalts, comprising high-Ti, low-Ti and KREEP-rich varieties. Chromium isotope ratios (δ53Cr) for mare basalts are positively correlated with indices of magmatic differentiation such as Mg# and Cr concentration which suggests that Cr isotopes were fractionated during magmatic differentiation. Modelling of the results provides evidence that spinel and pyroxene are the main phases controlling the Cr isotopic composition during fractional crystallisation. The most evolved samples have the lightest isotopic compositions, complemented by cumulates that are isotopically heavy. Two hypotheses are proposed to explain this fractionation: (i) equilibrium fractionation where heavy isotopes are preferentially incorporated into the spinel lattice and (ii) a difference in isotopic composition between Cr2+ and Cr3+ in the melt. However, both processes require magmatic temperatures below 1200 °C for appreciable Cr3+ to be present at the low oxygen fugacities found in the Moon (IW -1 to -2 log units). There is no isotopic difference between the most primitive high-Ti, low-Ti and KREEP basalts, which suggest that the sources of these basalts were homogeneous in terms of stable Cr isotopes. The least differentiated sample in our sample set is the low-Ti basalt 12016, characterised by a Cr isotopic composition of -0.222 ± 0.025‰, which is within error of the current BSE value (-0.124 ± 0.101‰). The similarity between the mantles of the Moon and Earth is consistent with a terrestrial origin for a major fraction of the lunar Cr. This similarity also suggests that Cr isotopes were not fractionated by core formation on the Moon.

What determines the impact of context on sequential action?

NARCIS (Netherlands)

Ruitenberg, M.F.L.; Verwey, Willem B.; Abrahamse, E.L.

2015-01-01

In the current study we build on earlier observations that memory-based sequential action is better in the original learning context than in other contexts. We examined whether changes in the perceptual context have differential impact across distinct processing phases (preparation versus execution

Alexander fractional differential window filter for ECG denoising.

Science.gov (United States)

Verma, Atul Kumar; Saini, Indu; Saini, Barjinder Singh

2018-06-01

The electrocardiogram (ECG) non-invasively monitors the electrical activities of the heart. During the process of recording and transmission, ECG signals are often corrupted by various types of noises. Minimizations of these noises facilitate accurate detection of various anomalies. In the present paper, Alexander fractional differential window (AFDW) filter is proposed for ECG signal denoising. The designed filter is based on the concept of generalized Alexander polynomial and the R-L differential equation of fractional calculus. This concept is utilized to formulate a window that acts as a forward filter. Thereafter, the backward filter is constructed by reversing the coefficients of the forward filter. The proposed AFDW filter is then obtained by averaging of the forward and backward filter coefficients. The performance of the designed AFDW filter is validated by adding the various type of noise to the original ECG signal obtained from MIT-BIH arrhythmia database. The two non-diagnostic measure, i.e., SNR, MSE, and one diagnostic measure, i.e., wavelet energy based diagnostic distortion (WEDD) have been employed for the quantitative evaluation of the designed filter. Extensive experimentations on all the 48-records of MIT-BIH arrhythmia database resulted in average SNR of 22.014 ± 3.806365, 14.703 ± 3.790275, 13.3183 ± 3.748230; average MSE of 0.001458 ± 0.00028, 0.0078 ± 0.000319, 0.01061 ± 0.000472; and average WEDD value of 0.020169 ± 0.01306, 0.1207 ± 0.061272, 0.1432 ± 0.073588, for ECG signal contaminated by the power line, random, and the white Gaussian noise respectively. A new metric named as morphological power preservation measure (MPPM) is also proposed that account for the power preservance (as indicated by PSD plots) and the QRS morphology. The proposed AFDW filter retained much of the original (clean) signal power without any significant morphological distortion as validated by MPPM measure that were 0

Exact Solutions of a Fractional-Type Differential-Difference Equation Related to Discrete MKdV Equation

International Nuclear Information System (INIS)

Aslan İsmail

2014-01-01

The extended simplest equation method is used to solve exactly a new differential-difference equation of fractional-type, proposed by Narita [J. Math. Anal. Appl. 381 (2011) 963] quite recently, related to the discrete MKdV equation. It is shown that the model supports three types of exact solutions with arbitrary parameters: hyperbolic, trigonometric and rational, which have not been reported before. (general)

On mixed derivatives type high dimensional multi-term fractional partial differential equations approximate solutions

Science.gov (United States)

Talib, Imran; Belgacem, Fethi Bin Muhammad; Asif, Naseer Ahmad; Khalil, Hammad

2017-01-01

In this research article, we derive and analyze an efficient spectral method based on the operational matrices of three dimensional orthogonal Jacobi polynomials to solve numerically the mixed partial derivatives type multi-terms high dimensions generalized class of fractional order partial differential equations. We transform the considered fractional order problem to an easily solvable algebraic equations with the aid of the operational matrices. Being easily solvable, the associated algebraic system leads to finding the solution of the problem. Some test problems are considered to confirm the accuracy and validity of the proposed numerical method. The convergence of the method is ensured by comparing our Matlab software simulations based obtained results with the exact solutions in the literature, yielding negligible errors. Moreover, comparative results discussed in the literature are extended and improved in this study.

THE NEW SOLUTION OF TIME FRACTIONAL WAVE EQUATION WITH CONFORMABLE FRACTIONAL DERIVATIVE DEFINITION

OpenAIRE

Çenesiz, Yücel; Kurt, Ali

2015-01-01

– In this paper, we used new fractional derivative definition, the conformable fractional derivative, for solving two and three dimensional time fractional wave equation. This definition is simple and very effective in the solution procedures of the fractional differential equations that have complicated solutions with classical fractional derivative definitions like Caputo, Riemann-Liouville and etc. The results show that conformable fractional derivative definition is usable and convenient ...

Fractional vector calculus and fluid mechanics

Science.gov (United States)

Lazopoulos, Konstantinos A.; Lazopoulos, Anastasios K.

2017-04-01

Basic fluid mechanics equations are studied and revised under the prism of fractional continuum mechanics (FCM), a very promising research field that satisfies both experimental and theoretical demands. The geometry of the fractional differential has been clarified corrected and the geometry of the fractional tangent spaces of a manifold has been studied in Lazopoulos and Lazopoulos (Lazopoulos KA, Lazopoulos AK. Progr. Fract. Differ. Appl. 2016, 2, 85-104), providing the bases of the missing fractional differential geometry. Therefore, a lot can be contributed to fractional hydrodynamics: the basic fractional fluid equations (Navier Stokes, Euler and Bernoulli) are derived and fractional Darcy's flow in porous media is studied.

Fractional Processes and Fractional-Order Signal Processing Techniques and Applications

CERN Document Server

Sheng, Hu; Qiu, TianShuang

2012-01-01

Fractional processes are widely found in science, technology and engineering systems. In Fractional Processes and Fractional-order Signal Processing, some complex random signals, characterized by the presence of a heavy-tailed distribution or non-negligible dependence between distant observations (local and long memory), are introduced and examined from the ‘fractional’ perspective using simulation, fractional-order modeling and filtering and realization of fractional-order systems. These fractional-order signal processing (FOSP) techniques are based on fractional calculus, the fractional Fourier transform and fractional lower-order moments. Fractional Processes and Fractional-order Signal Processing: • presents fractional processes of fixed, variable and distributed order studied as the output of fractional-order differential systems; • introduces FOSP techniques and the fractional signals and fractional systems point of view; • details real-world-application examples of FOSP techniques to demonstr...

Assessment of the BCR sequential extraction procedure for thallium fractionation using synthetic mineral mixtures

Czech Academy of Sciences Publication Activity Database

Vaněk, A.; Grygar, Tomáš; Chrastný, V.; Tejnecký, V.; Drahota, Petr; Komárek, M.

2010-01-01

Roč. 176, 1-3 (2010), s. 913-918 ISSN 0304-3894 Institutional research plan: CEZ:AV0Z4032918; CEZ:AV0Z30130516 Keywords : Metal * Sequential extraction * Goethite * Ferrihydrite * Birnessite * Illite Subject RIV: DD - Geochemistry Impact factor: 3.723, year: 2010

Approximate rational Jacobi elliptic function solutions of the fractional differential equations via the enhanced Adomian decomposition method

International Nuclear Information System (INIS)

Song Lina; Wang Weiguo

2010-01-01

In this Letter, an enhanced Adomian decomposition method which introduces the h-curve of the homotopy analysis method into the standard Adomian decomposition method is proposed. Some examples prove that this method can derive successfully approximate rational Jacobi elliptic function solutions of the fractional differential equations.

Stable Numerical Approach for Fractional Delay Differential Equations

Science.gov (United States)

Singh, Harendra; Pandey, Rajesh K.; Baleanu, D.

2017-12-01

In this paper, we present a new stable numerical approach based on the operational matrix of integration of Jacobi polynomials for solving fractional delay differential equations (FDDEs). The operational matrix approach converts the FDDE into a system of linear equations, and hence the numerical solution is obtained by solving the linear system. The error analysis of the proposed method is also established. Further, a comparative study of the approximate solutions is provided for the test examples of the FDDE by varying the values of the parameters in the Jacobi polynomials. As in special case, the Jacobi polynomials reduce to the well-known polynomials such as (1) Legendre polynomial, (2) Chebyshev polynomial of second kind, (3) Chebyshev polynomial of third and (4) Chebyshev polynomial of fourth kind respectively. Maximum absolute error and root mean square error are calculated for the illustrated examples and presented in form of tables for the comparison purpose. Numerical stability of the presented method with respect to all four kind of polynomials are discussed. Further, the obtained numerical results are compared with some known methods from the literature and it is observed that obtained results from the proposed method is better than these methods.

A Numerical Algorithm for Solving a Four-Point Nonlinear Fractional Integro-Differential Equations

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Er Gao

2012-01-01

Full Text Available We provide a new algorithm for a four-point nonlocal boundary value problem of nonlinear integro-differential equations of fractional order q∈(1,2] based on reproducing kernel space method. According to our work, the analytical solution of the equations is represented in the reproducing kernel space which we construct and so the n-term approximation. At the same time, the n-term approximation is proved to converge to the analytical solution. An illustrative example is also presented, which shows that the new algorithm is efficient and accurate.

Existence of Positive Solutions to a Singular Semipositone Boundary Value Problem of Nonlinear Fractional Differential Systems

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Xiaofeng Zhang

2017-12-01

Full Text Available In this paper, we consider the existence of positive solutions to a singular semipositone boundary value problem of nonlinear fractional differential equations. By applying the fixed point index theorem, some new results for the existence of positive solutions are obtained. In addition, an example is presented to demonstrate the application of our main results.

Simultaneous optimization of sequential IMRT plans

International Nuclear Information System (INIS)

Popple, Richard A.; Prellop, Perri B.; Spencer, Sharon A.; Santos, Jennifer F. de los; Duan, Jun; Fiveash, John B.; Brezovich, Ivan A.

2005-01-01

Radiotherapy often comprises two phases, in which irradiation of a volume at risk for microscopic disease is followed by a sequential dose escalation to a smaller volume either at a higher risk for microscopic disease or containing only gross disease. This technique is difficult to implement with intensity modulated radiotherapy, as the tolerance doses of critical structures must be respected over the sum of the two plans. Techniques that include an integrated boost have been proposed to address this problem. However, clinical experience with such techniques is limited, and many clinicians are uncomfortable prescribing nonconventional fractionation schemes. To solve this problem, we developed an optimization technique that simultaneously generates sequential initial and boost IMRT plans. We have developed an optimization tool that uses a commercial treatment planning system (TPS) and a high level programming language for technical computing. The tool uses the TPS to calculate the dose deposition coefficients (DDCs) for optimization. The DDCs were imported into external software and the treatment ports duplicated to create the boost plan. The initial, boost, and tolerance doses were specified and used to construct cost functions. The initial and boost plans were optimized simultaneously using a gradient search technique. Following optimization, the fluence maps were exported to the TPS for dose calculation. Seven patients treated using sequential techniques were selected from our clinical database. The initial and boost plans used to treat these patients were developed independently of each other by dividing the tolerance doses proportionally between the initial and boost plans and then iteratively optimizing the plans until a summation that met the treatment goals was obtained. We used the simultaneous optimization technique to generate plans that met the original planning goals. The coverage of the initial and boost target volumes in the simultaneously optimized

Sequential extraction of uranium metal contamination

International Nuclear Information System (INIS)

Murry, M.M.; Spitz, H.B.; Connick, W.B.

2016-01-01

Samples of uranium contaminated dirt collected from the dirt floor of an abandoned metal rolling mill were analyzed for uranium using a sequential extraction protocol involving a series of five increasingly aggressive solvents. The quantity of uranium extracted from the contaminated dirt by each reagent can aid in predicting the fate and transport of the uranium contamination in the environment. Uranium was separated from each fraction using anion exchange, electrodeposition and analyzed by alpha spectroscopy analysis. Results demonstrate that approximately 77 % of the uranium was extracted using NH 4 Ac in 25 % acetic acid. (author)

Fractional RC and LC Electrical Circuits

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Gómez-Aguilar José Francisco

2014-04-01

Full Text Available In this paper we propose a fractional differential equation for the electrical RC and LC circuit in terms of the fractional time derivatives of the Caputo type. The order of the derivative being considered is 0 < ɣ ≤1. To keep the dimensionality of the physical parameters R, L, C the new parameter σ is introduced. This parameter characterizes the existence of fractional structures in the system. A relation between the fractional order time derivative ɣ and the new parameter σ is found. The numeric Laplace transform method was used for the simulation of the equations results. The results show that the fractional differential equations generalize the behavior of the charge, voltage and current depending of the values of ɣ. The classical cases are recovered by taking the limit when ɣ = 1. An analysis in the frequency domain of an RC circuit shows the application and use of fractional order differential equations.

Fractional Stochastic Field Theory

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Honkonen, Juha

2018-02-01

Models describing evolution of physical, chemical, biological, social and financial processes are often formulated as differential equations with the understanding that they are large-scale equations for averages of quantities describing intrinsically random processes. Explicit account of randomness may lead to significant changes in the asymptotic behaviour (anomalous scaling) in such models especially in low spatial dimensions, which in many cases may be captured with the use of the renormalization group. Anomalous scaling and memory effects may also be introduced with the use of fractional derivatives and fractional noise. Construction of renormalized stochastic field theory with fractional derivatives and fractional noise in the underlying stochastic differential equations and master equations and the interplay between fluctuation-induced and built-in anomalous scaling behaviour is reviewed and discussed.

The Initial Conditions of Fractional Calculus

International Nuclear Information System (INIS)

Trigeassou, J. C.; Maamri, N.

2011-01-01

During the past fifty years , Fractional Calculus has become an original and renowned mathematical tool for the modelling of diffusion Partial Differential Equations and the design of robust control algorithms. However, in spite of these celebrated results, some theoretical problems have not yet received a satisfying solution. The mastery of initial conditions, either for Fractional Differential Equations (FDEs) or for the Caputo and Riemann-Liouville fractional derivatives, remains an open research domain. The solution of this fundamental problem, also related to the long range memory property, is certainly the necessary prerequisite for a satisfying approach to modelling and control applications. The fractional integrator and its continuously frequency distributed differential model is a valuable tool for the simulation of fractional systems and the solution of initial condition problems. Indeed, the infinite dimensional state vector of fractional integrators allows the direct generalization to fractional calculus of the theoretical results of integer order systems. After a reminder of definitions and properties related to fractional derivatives and systems, this presentation is intended to show, based on the results of two recent publications [1,2], how the fractional integrator provides the solution of the initial condition problem of FDEs and of Caputo and Riemann-Liouville fractional derivatives. Numerical simulation examples illustrate and validate these new theoretical concepts.

Comparison of three sequential extraction procedures to describe metal fractionation in anaerobic granular sludges

NARCIS (Netherlands)

Hullebusch, van E.D.; Sudarno, S.; Zandvoort, M.H.; Lens, P.N.L.

2005-01-01

In the last few decades. several sequential extraction procedures have been developed to quantify the chemical status of metals in the solid phase. In this study. three extraction techniques (modified [A. Tessier, P.G.C. Campbell, M. Bisson, Anal. Chem. 51 (1979) 844]: [R.C. Stover. L.E. Sommers,

Solid phase speciation of arsenic by sequential extraction in standard reference materials and industrially contaminated soil samples

International Nuclear Information System (INIS)

Herreweghe, Samuel van; Swennen, Rudy; Vandecasteele, Carlo; Cappuyns, Valerie

2003-01-01

Leaching experiments, a mineralogical survey and larger samples are preferred when arsenic is present as discrete mineral phases. - Availability, mobility, (phyto)toxicity and potential risk of contaminants is strongly affected by the manner of appearance of elements, the so-called speciation. Operational fractionation methods like sequential extractions have been applied for a long time to determine the solid phase speciation of heavy metals since direct determination of specific chemical compounds can not always be easily achieved. The three-step sequential extraction scheme recommended by the BCR and two extraction schemes based on the phosphorus-like protocol proposed by Manful (1992, Occurrence and Ecochemical Behaviours of Arsenic in a Goldsmelter Impacted Area in Ghana, PhD dissertation, at the RUG) were applied to four standard reference materials (SRM) and to a batch of samples from industrially contaminated sites, heavily contaminated with arsenic and heavy metals. The SRM 2710 (Montana soil) was found to be the most useful reference material for metal (Mn, Cu, Zn, As, Cd and Pb) fractionation using the BCR sequential extraction procedure. Two sequential extraction schemes were developed and compared for arsenic with the aim to establish a better fractionation and recovery rate than the BCR-scheme for this element in the SRM samples. The major part of arsenic was released from the heavily contaminated samples after NaOH-extraction. Inferior extraction variability and recovery in the heavily contaminated samples compared to SRMs could be mainly contributed to subsample heterogeneity

Selenium Speciation Assessed by X-Ray Absorption Spectroscopy of Sequentially Extracted Anaerobic Biofilms

NARCIS (Netherlands)

Lenz, M.; Hullebusch, van E.D.; Farges, F.; Nikitenko, S.; Borca, C.N.; Grolimund, D.; Lens, P.N.L.

2008-01-01

Wet chemical methods such as sequential extraction procedures are commonly used to assess selenium fractionation in anoxic environments, allowing an estimation of the mobility and bioavailability of selenium. However, the interpretation can be biased by unselective extraction of targeted species and

A Mixed Monotone Operator Method for the Existence and Uniqueness of Positive Solutions to Impulsive Caputo Fractional Differential Equations

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Jieming Zhang

2013-01-01

Full Text Available We establish some sufficient conditions for the existence and uniqueness of positive solutions to a class of initial value problem for impulsive fractional differential equations involving the Caputo fractional derivative. Our analysis relies on a fixed point theorem for mixed monotone operators. Our result can not only guarantee the existence of a unique positive solution but also be applied to construct an iterative scheme for approximating it. An example is given to illustrate our main result.

Boundary value problemfor multidimensional fractional advection-dispersion equation

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Khasambiev Mokhammad Vakhaevich

2015-05-01

Full Text Available In recent time there is a very great interest in the study of differential equations of fractional order, in which the unknown function is under the symbol of fractional derivative. It is due to the development of the theory of fractional integro-differential theory and application of it in different fields.The fractional integrals and derivatives of fractional integro-differential equations are widely used in modern investigations of theoretical physics, mechanics, and applied mathematics. The fractional calculus is a very powerful tool for describing physical systems, which have a memory and are non-local. Many processes in complex systems have nonlocality and long-time memory. Fractional integral operators and fractional differential operators allow describing some of these properties. The use of the fractional calculus will be helpful for obtaining the dynamical models, in which integro-differential operators describe power long-time memory by time and coordinates, and three-dimensional nonlocality for complex medium and processes.Differential equations of fractional order appear when we use fractal conception in physics of the condensed medium. The transfer, described by the operator with fractional derivatives at a long distance from the sources, leads to other behavior of relatively small concentrations as compared with classic diffusion. This fact redefines the existing ideas about safety, based on the ideas on exponential velocity of damping. Fractional calculus in the fractal theory and the systems with memory have the same importance as the classic analysis in mechanics of continuous medium.In recent years, the application of fractional derivatives for describing and studying the physical processes of stochastic transfer is very popular too. Many problems of filtration of liquids in fractal (high porous medium lead to the need to study boundary value problems for partial differential equations in fractional order.In this paper the

Numerical analysis for trajectory controllability of a coupled multi-order fractional delay differential system via the shifted Jacobi method

Science.gov (United States)

Priya, B. Ganesh; Muthukumar, P.

2018-02-01

This paper deals with the trajectory controllability for a class of multi-order fractional linear systems subject to a constant delay in state vector. The solution for the coupled fractional delay differential equation is established by the Mittag-Leffler function. The necessary and sufficient condition for the trajectory controllability is formulated and proved by the generalized Gronwall's inequality. The approximate trajectory for the proposed system is obtained through the shifted Jacobi operational matrix method. The numerical simulation of the approximate solution shows the theoretical results. Finally, some remarks and comments on the existing results of constrained controllability for the fractional dynamical system are also presented.

Exact solutions of time-fractional heat conduction equation by the fractional complex transform

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Li Zheng-Biao

2012-01-01

Full Text Available The Fractional Complex Transform is extended to solve exactly time-fractional differential equations with the modified Riemann-Liouville derivative. How to incorporate suitable boundary/initial conditions is also discussed.

Diffusion with space memory modelled with distributed order space fractional differential equations

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M. Caputo

2003-06-01

Full Text Available Distributed order fractional differential equations (Caputo, 1995, 2001; Bagley and Torvik, 2000a,b were fi rst used in the time domain; they are here considered in the space domain and introduced in the constitutive equation of diffusion. The solution of the classic problems are obtained, with closed form formulae. In general, the Green functions act as low pass fi lters in the frequency domain. The major difference with the case when a single space fractional derivative is present in the constitutive equations of diffusion (Caputo and Plastino, 2002 is that the solutions found here are potentially more fl exible to represent more complex media (Caputo, 2001a. The difference between the space memory medium and that with the time memory is that the former is more fl exible to represent local phenomena while the latter is more fl exible to represent variations in space. Concerning the boundary value problem, the difference with the solution of the classic diffusion medium, in the case when a constant boundary pressure is assigned and in the medium the pressure is initially nil, is that one also needs to assign the fi rst order space derivative at the boundary.

Fractional approximations for linear first order differential equation with polynomial coefficients-application to E1(x) and Z(s)

International Nuclear Information System (INIS)

Martin, P.; Zamudio-Cristi, J.

1982-01-01

A method is described to obtain fractional approximations for linear first order differential equations with polynomial coefficients. This approximation can give good accuracy in a large region of the complex variable plane that may include all the real axis. The parameters of the approximation are solutions of algebraic equations obtained through the coefficients of the highest and lowest power of the variable after the sustitution of the fractional approximation in the differential equation. The method is more general than the asymptotical Pade method, and it is not required to determine the power series or asymptotical expansion. A simple approximation for the exponential integral is found, which give three exact digits for most of the real values of the variable. Approximations of higher accuracy and of the same degree than other authors are also obtained. (Author) [pt

The Tocotrienol-Rich Fraction Is Superior to Tocopherol in Promoting Myogenic Differentiation in the Prevention of Replicative Senescence of Myoblasts.

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Shy Cian Khor

Full Text Available Aging results in a loss of muscle mass and strength. Myoblasts play an important role in maintaining muscle mass through regenerative processes, which are impaired during aging. Vitamin E potentially ameliorates age-related phenotypes. Hence, this study aimed to determine the effects of the tocotrienol-rich fraction (TRF and α-tocopherol (ATF in protecting myoblasts from replicative senescence and promoting myogenic differentiation. Primary human myoblasts were cultured into young and senescent stages and were then treated with TRF or ATF for 24 h, followed by an analysis of cell proliferation, senescence biomarkers, cellular morphology and differentiation. Our data showed that replicative senescence impaired the normal regenerative processes of myoblasts, resulting in changes in cellular morphology, cell proliferation, senescence-associated β-galactosidase (SA-β-gal expression, myogenic differentiation and myogenic regulatory factors (MRFs expression. Treatment with both TRF and ATF was beneficial to senescent myoblasts in reclaiming the morphology of young cells, improved cell viability and decreased SA-β-gal expression. However, only TRF treatment increased BrdU incorporation in senescent myoblasts, as well as promoted myogenic differentiation through the modulation of MRFs at the mRNA and protein levels. MYOD1 and MYOG gene expression and myogenin protein expression were modulated in the early phases of myogenic differentiation. In conclusion, the tocotrienol-rich fraction is superior to α-tocopherol in ameliorating replicative senescence-related aberration and promoting differentiation via modulation of MRFs expression, indicating vitamin E potential in modulating replicative senescence of myoblasts.

Calculus of variations involving Caputo-Fabrizio fractional differentiation

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Nuno R. O. Bastos

2018-02-01

Full Text Available This paper is devoted to study some variational problems with functionals containing the Caputo-Fabrizio fractional derivative, that is a fractional derivative with a non-singular kernel.

Sonicated Protein Fractions of Mycoplasma hyopneumoniae Induce Inflammatory Responses and Differential Gene Expression in a Murine Alveolar Macrophage Cell Line.

Science.gov (United States)

Damte, Dereje; Lee, Seung-Jin; Birhanu, Biruk Tesfaye; Suh, Joo-Won; Park, Seung-Chun

2015-12-28

Mycoplasma hyopneumoniae is known to cause porcine enzootic pneumonia (EP), an important disease in swine production. The objective of this study was to examine the effects of sonicated protein fractions of M. hyopneumoniae on inflammatory response and gene expression in the murine alveolar macrophage MH-S cell line. The effects of sonicated protein fractions and intact M. hyopneumoniae on the gene expression of cytokines and iNOS were assessed using RT-PCR. The Annealing Control Primer (ACP)-based PCR method was used to screen differentially expressed genes. Increased transcription of interleukin (IL)-1β, IL-6, tumor necrosis factor (TNF)-α, COX-2, and iNOS mRNA was observed after exposure to the supernatant (SPT), precipitant (PPT), and intact M. hyopneumoniae protein. A time-dependent analysis of the mRNA expression revealed an upregulation after 4 h for IL-6 and iNOS and after 12 h for IL-1β and TNF-α, for both SPT and PPT; the fold change in COX-2 expression was less. A dose- and time-dependent correlation was observed in nitrite (NO) production for both protein fractions; however, there was no significant difference between the effects of the two protein fractions. In a differential gene analysis, PCR revealed differential expression for nine gene bands after 3 h of stimulation - only one gene was downregulated, while the remaining eight were upregulated. The results of this study provide insights that help improve our understanding of the mechanisms underlying the pathogenesis of and macrophage defenses against M. hyopneumoniae assault, and suggest targets for future studies on therapeutic interventions for M. hyopneumoniae infections.

Calorimetric and diffractometric evidence for the sequential crystallization of buffer components and the consequential pH swing in frozen solutions.

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Sundaramurthi, Prakash; Shalaev, Evgenyi; Suryanarayanan, Raj

2010-04-15

Sequential crystallization of succinate buffer components in the frozen solution has been studied by differential scanning calorimetry and X-ray diffractometry (both laboratory and synchrotron sources). The consequential pH shifts were monitored using a low-temperature electrode. When a solution buffered to pH pK(a)(2), the freeze-concentrate pH first decreased and then increased due to the sequential crystallization of the basic (disodium succinate) followed by the acidic (monosodium succinate and succinic acid) buffer components. XRD provided direct evidence of the crystallization events in the frozen buffer solutions, including the formation of disodium succinate hexahydrate [Na(2)(CH(2)COO)(2).6H(2)O]. When the frozen solution was warmed in a differential scanning calorimeter, multiple endotherms attributable to the melting of buffer components and ice were observed. When the frozen solutions were dried under reduced pressure, ice sublimation was followed by dehydration of the crystalline hexahydrate to a poorly crystalline anhydrate. However, crystalline succinic acid and monosodium succinate were retained in the final lyophiles. The pH and the buffer salt concentration of the prelyo solution influenced the crystalline salt content in the final lyophile. The direction and magnitude of the pH shift in the frozen solution depended on both the initial pH and the buffer concentration. In light of the pH-sensitive nature of a significant fraction of pharmaceuticals (especially proteins), extreme care is needed in both the buffer selection and its concentration.

Chebyshev Finite Difference Method for Fractional Boundary Value Problems

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Boundary

2015-09-01

Full Text Available This paper presents a numerical method for fractional differential equations using Chebyshev finite difference method. The fractional derivatives are described in the Caputo sense. Numerical results show that this method is of high accuracy and is more convenient and efficient for solving boundary value problems involving fractional ordinary differential equations. AMS Subject Classification: 34A08 Keywords and Phrases: Chebyshev polynomials, Gauss-Lobatto points, fractional differential equation, finite difference 1. Introduction The idea of a derivative which interpolates between the familiar integer order derivatives was introduced many years ago and has gained increasing importance only in recent years due to the development of mathematical models of a certain situations in engineering, materials science, control theory, polymer modelling etc. For example see [20, 22, 25, 26]. Most fractional order differential equations describing real life situations, in general do not have exact analytical solutions. Several numerical and approximate analytical methods for ordinary differential equation Received: December 2014; Accepted: March 2015 57 Journal of Mathematical Extension Vol. 9, No. 3, (2015, 57-71 ISSN: 1735-8299 URL: http://www.ijmex.com Chebyshev Finite Difference Method for Fractional Boundary Value Problems H. Azizi Taft Branch, Islamic Azad University Abstract. This paper presents a numerical method for fractional differential equations using Chebyshev finite difference method. The fractional derivative

Electronic realization of the fractional-order systems

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Františka Dorčáková

2007-10-01

Full Text Available This article is devoted to the electronic (analogue realization of the fractional-order systems – controllers or controlled objects whose we earlier used, identified, and analyzed as a mathematical models only ��� namely a fractional-order differential equation, and solved numerically using a method based on the truncated version of the Grunwald - Letnikov formula for fractional derivative. The electronic realization of the fractional derivative is based on the continued fraction expansion of the rational approximation of the fractional differentiator from which we obtained the values of the resistors and capacitors of the electronic circuit. Along with the mathematical description are presented also simulation and measurement results.

Evaluation of the readsorption of plutonium and americium in dynamic fractionations of environmental solid samples

DEFF Research Database (Denmark)

Petersen, Roongrat; Hou, Xiaolin; Hansen, Elo Harald

2008-01-01

A dynamic extraction system exploiting sequential injection (SI) for sequential extractions incorporating a specially designed extraction column is developed to fractionate radionuclides in environmental solid samples such as soils and sediments. The extraction column can contain a large amount...... of soil sample (up to 5 g), and under optimal operational conditions it does not give rise to creation of back pressure. Attention has been placed on studies of the readsorption problems during sequential extraction using a modified Standards, Measurements and Testing (SM&T) scheme with 4-step sequential...

Proton density fat fraction (PDFF) MRI for differentiation of benign and malignant vertebral lesions.

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Schmeel, Frederic Carsten; Luetkens, Julian Alexander; Wagenhäuser, Peter Johannes; Meier-Schroers, Michael; Kuetting, Daniel Lloyd; Feißt, Andreas; Gieseke, Jürgen; Schmeel, Leonard Christopher; Träber, Frank; Schild, Hans Heinz; Kukuk, Guido Matthias

2018-06-01

To investigate whether proton density fat fraction (PDFF) measurements using a six-echo modified Dixon sequence can help to differentiate between benign and malignant vertebral bone marrow lesions. Sixty-six patients were prospectively enrolled in our study. In addition to conventional MRI at 3.0-Tesla including at least sagittal T2-weighted/spectral attenuated inversion recovery and T1-weighted sequences, all patients underwent a sagittal six-echo modified Dixon sequence of the spine. The mean PDFF was calculated using regions of interest and compared between vertebral lesions. A cut-off value of 6.40% in PDFF was determined by receiver operating characteristic curves and used to differentiate between malignant (benign and malignant vertebral lesions with a high diagnostic accuracy. • Establishing a diagnosis of indeterminate vertebral lesions is a common clinical problem • Benign bone marrow processes may mimic the signal alterations observed in malignancy • PDFF differentiates between benign and malignant lesions with a high diagnostic accuracy • PDFF of non-neoplastic vertebral lesions is significantly higher than that of malignancy • PDFF from six-echo modified Dixon may help avoid potentially harmful bone biopsy.

Second-order numerical methods for multi-term fractional differential equations: Smooth and non-smooth solutions

Science.gov (United States)

Zeng, Fanhai; Zhang, Zhongqiang; Karniadakis, George Em

2017-12-01

Starting with the asymptotic expansion of the error equation of the shifted Gr\\"{u}nwald--Letnikov formula, we derive a new modified weighted shifted Gr\\"{u}nwald--Letnikov (WSGL) formula by introducing appropriate correction terms. We then apply one special case of the modified WSGL formula to solve multi-term fractional ordinary and partial differential equations, and we prove the linear stability and second-order convergence for both smooth and non-smooth solutions. We show theoretically and numerically that numerical solutions up to certain accuracy can be obtained with only a few correction terms. Moreover, the correction terms can be tuned according to the fractional derivative orders without explicitly knowing the analytical solutions. Numerical simulations verify the theoretical results and demonstrate that the new formula leads to better performance compared to other known numerical approximations with similar resolution.

SPF-RR sequential photothermal fractional resurfacing and remodeling with the variable pulse Er:YAG laser and scanner-assisted Nd:YAG laser.

Science.gov (United States)

Marini, Leonardo

2009-12-01

Many different lasers, polychromatic high-intensity light sources (PCLs), and RF devices have claimed clinical efficacy in rejuvenating the skin. In this study, the sequential combination of two different laser wavelengths was evaluated to produce reliably significant clinical improvements optimizing treatment parameters. The left volar aspects of the forearms of four volunteers were treated with nine different parameter settings using a variable pulsewidth fractional Er:YAG 2940-nm laser with and without air cooling. The pain perception level was recorded on a 0-10 point scale (0=No pain; 10=Most severe pain). Three evaluations were made: during treatment, immediately after treatment, and 5 minutes after treatment. The same investigation was made on the right volar aspects of the same four volunteers using a short-pulse, random pattern, 3-mm spot, scanner-assisted Nd-YAG 1064-nm laser at 0.3 ms pulsewidth at seven different parameter settings. Clinical evaluations were made concerning erythema and edema 3 days after treatment, as well as pre-operative and 60 days postoperative skin texture plus color uniformity. Considering that the majority of cosmetic patients are willing to accept a relatively short and uneventful downtime (2-4 days according to a study we are presently conducting) and do prefer to limit their intra- and postoperative pain to a minimum, the best combination of clinical improvement matching these two important parameters were selected for our study. A treatment strategy combining two sequential passes of long-pulse Nd:YAG laser (Nd:YAG-LP) at 0.3 and 35 ms followed by two passes of long-pulse fractional Er:YAG laser (Er:YAG-FT) at 600 micros was designed to treat the facial regions of 10 volunteers affected by a combination of intrinsic (chrono-) and extrinsic (mostly photo-) aging. The pain perception level was recorded on a 0-10 scale (0=No pain; 10=Most severe pain). Three evaluations were made: during, immediately after, and 5 minutes after

MUSCLE OR MOTIVATION? A STOP SIGNAL STUDY ON THE EFFECTS OF SEQUENTIAL COGNITIVE CONTROL

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Hilde M. Huizenga

2012-05-01

Full Text Available Performance in cognitive control tasks deteriorates when these tasks are performed together with other tasks that also require cognitive control, that is, if simultaneous cognitive control is required. Surprisingly, this decrease in performance is also observed if tasks are preceded by other cognitive control tasks, that is, if sequential cognitive control is required. The common explanation for the latter finding is that previous acts of cognitive control deplete a common resource, just like a muscle becomes fatigued after repeated use. An alternative explanation however has also been put forward, namely that repeated acts of cognitive control reduce the motivation to match allocated resources to required resources. In this paper we formalize these two accounts, the muscle and the motivation account, and show that they yield differential predictions on the interaction between simultaneous and sequential cognitive control. Such an interaction is not predicted by the muscle account, whereas it is predicted by the motivation account.These predictions were tested in a paradigm where participants had to perform a series of stop-signal tasks, these tasks varied both in their demands on simultaneous control and in their demands on sequential control. This paradigm, combined with a multilevel analysis, offered the possibility to test the differential predictions directly. Results of two studies indicate that an interaction between simultaneous and sequential cognitive control is present. Therefore it is concluded that effects of sequential cognitive control are best explained by the motivation account.

Sequential fractionation and isolation of subcellular proteins from tissue or cultured cells

OpenAIRE

Sabina Baghirova; Bryan G. Hughes; Michael J. Hendzel; Richard Schulz

2015-01-01

Many types of studies require the localization of a protein to, or isolation of enriched protein from a specific cellular compartment. Many protocols in the literature and from commercially available kits claim to yield pure cellular fractions. However, in our hands, the former often do not work effectively and the latter may be prohibitively expensive if a large number of fractionations are required. Furthermore, the largely proprietary composition of reagents in commercial kits means that t...

Basal ganglia and cortical networks for sequential ordering and rhythm of complex movements

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Jeffery G. Bednark

2015-07-01

Full Text Available Voluntary actions require the concurrent engagement and coordinated control of complex temporal (e.g. rhythm and ordinal motor processes. Using high-resolution functional magnetic resonance imaging (fMRI and multi-voxel pattern analysis (MVPA, we sought to determine the degree to which these complex motor processes are dissociable in basal ganglia and cortical networks. We employed three different finger-tapping tasks that differed in the demand on the sequential temporal rhythm or sequential ordering of submovements. Our results demonstrate that sequential rhythm and sequential order tasks were partially dissociable based on activation differences. The sequential rhythm task activated a widespread network centered around the SMA and basal-ganglia regions including the dorsomedial putamen and caudate nucleus, while the sequential order task preferentially activated a fronto-parietal network. There was also extensive overlap between sequential rhythm and sequential order tasks, with both tasks commonly activating bilateral premotor, supplementary motor, and superior/inferior parietal cortical regions, as well as regions of the caudate/putamen of the basal ganglia and the ventro-lateral thalamus. Importantly, within the cortical regions that were active for both complex movements, MVPA could accurately classify different patterns of activation for the sequential rhythm and sequential order tasks. In the basal ganglia, however, overlapping activation for the sequential rhythm and sequential order tasks, which was found in classic motor circuits of the putamen and ventro-lateral thalamus, could not be accurately differentiated by MVPA. Overall, our results highlight the convergent architecture of the motor system, where complex motor information that is spatially distributed in the cortex converges into a more compact representation in the basal ganglia.

The Ground Flash Fraction Retrieval Algorithm Employing Differential Evolution: Simulations and Applications

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Koshak, William; Solakiewicz, Richard

2012-01-01

The ability to estimate the fraction of ground flashes in a set of flashes observed by a satellite lightning imager, such as the future GOES-R Geostationary Lightning Mapper (GLM), would likely improve operational and scientific applications (e.g., severe weather warnings, lightning nitrogen oxides studies, and global electric circuit analyses). A Bayesian inversion method, called the Ground Flash Fraction Retrieval Algorithm (GoFFRA), was recently developed for estimating the ground flash fraction. The method uses a constrained mixed exponential distribution model to describe a particular lightning optical measurement called the Maximum Group Area (MGA). To obtain the optimum model parameters (one of which is the desired ground flash fraction), a scalar function must be minimized. This minimization is difficult because of two problems: (1) Label Switching (LS), and (2) Parameter Identity Theft (PIT). The LS problem is well known in the literature on mixed exponential distributions, and the PIT problem was discovered in this study. Each problem occurs when one allows the numerical minimizer to freely roam through the parameter search space; this allows certain solution parameters to interchange roles which leads to fundamental ambiguities, and solution error. A major accomplishment of this study is that we have employed a state-of-the-art genetic-based global optimization algorithm called Differential Evolution (DE) that constrains the parameter search in such a way as to remove both the LS and PIT problems. To test the performance of the GoFFRA when DE is employed, we applied it to analyze simulated MGA datasets that we generated from known mixed exponential distributions. Moreover, we evaluated the GoFFRA/DE method by applying it to analyze actual MGAs derived from low-Earth orbiting lightning imaging sensor data; the actual MGA data were classified as either ground or cloud flash MGAs using National Lightning Detection Network[TM] (NLDN) data. Solution error

Similarity Solutions for Multiterm Time-Fractional Diffusion Equation

OpenAIRE

Elsaid, A.; Abdel Latif, M. S.; Maneea, M.

2016-01-01

Similarity method is employed to solve multiterm time-fractional diffusion equation. The orders of the fractional derivatives belong to the interval (0,1] and are defined in the Caputo sense. We illustrate how the problem is reduced from a multiterm two-variable fractional partial differential equation to a multiterm ordinary fractional differential equation. Power series solution is obtained for the resulting ordinary problem and the convergence of the series solution is discussed. Based on ...

Generation of multi-wing chaotic attractor in fractional order system

International Nuclear Information System (INIS)

Zhang Chaoxia; Yu Simin

2011-01-01

Highlights: → We investigate a novel approach for generating multi-wing chaotic attractors. → We introduce a fundamental fractional differential nominal linear system. → A proper nonlinear state feedback controller is designed. → The controlled system can generate fractional-order multi-wing chaotic attractors. - Abstract: In this paper, a novel approach is proposed for generating multi-wing chaotic attractors from the fractional linear differential system via nonlinear state feedback controller equipped with a duality-symmetric multi-segment quadratic function. The main idea is to design a proper nonlinear state feedback controller by using four construction criterions from a fundamental fractional differential nominal linear system, so that the controlled fractional differential system can generate multi-wing chaotic attractors. It is the first time in the literature to report the multi-wing chaotic attractors from an uncoupled fractional differential system. Furthermore, some basic dynamical analysis and numerical simulations are also given, confirming the effectiveness of the proposed method.

Fractional dynamic calculus and fractional dynamic equations on time scales

CERN Document Server

Georgiev, Svetlin G

2018-01-01

Pedagogically organized, this monograph introduces fractional calculus and fractional dynamic equations on time scales in relation to mathematical physics applications and problems. Beginning with the definitions of forward and backward jump operators, the book builds from Stefan Hilger’s basic theories on time scales and examines recent developments within the field of fractional calculus and fractional equations. Useful tools are provided for solving differential and integral equations as well as various problems involving special functions of mathematical physics and their extensions and generalizations in one and more variables. Much discussion is devoted to Riemann-Liouville fractional dynamic equations and Caputo fractional dynamic equations.  Intended for use in the field and designed for students without an extensive mathematical background, this book is suitable for graduate courses and researchers looking for an introduction to fractional dynamic calculus and equations on time scales. .

Exact Solutions of Fractional Burgers and Cahn-Hilliard Equations Using Extended Fractional Riccati Expansion Method

Directory of Open Access Journals (Sweden)

Wei Li

2014-01-01

Full Text Available Based on a general fractional Riccati equation and with Jumarie’s modified Riemann-Liouville derivative to an extended fractional Riccati expansion method for solving the time fractional Burgers equation and the space-time fractional Cahn-Hilliard equation, the exact solutions expressed by the hyperbolic functions and trigonometric functions are obtained. The obtained results show that the presented method is effective and appropriate for solving nonlinear fractional differential equations.

Speciation of heavy metals in garden soils. Evidences from selective and sequential chemical leaching

Energy Technology Data Exchange (ETDEWEB)

Cheng, Zhongqi; Lee, Leda; Dayan, Sara; Grinshtein, Michael [Brooklyn College of The City Univ. of New York, Brooklyn, NY (United States). Environmental Sciences Analytical Cnter; Shaw, Richard [USDA-NRCS NYC Soil Survey, Staten Island, NY (United States)

2011-06-15

Purpose: Gardening (especially food growing) in urban areas is becoming popular, but urban soils are often very contaminated for historical reasons. There is lack of sufficient information as to the bioavailability of soil heavy metals to plants and human in urban environments. This study examines the relative leachability of Cr, Ni, As, Cd, Zn, and Pb for soils with varying characteristics. The speciation and mobility of these metals can be qualitatively inferred from the leaching experiments. The goal is to use the data to shed some light on their bioavailability to plant and human, as well as the basis for soil remediation. Materials and methods: Selective and sequential chemical leaching methods were both used to evaluate the speciation of Cr, Ni, As, Cd, Zn, and Pb in soil samples collected from New York City residential and community gardens. The sequential leaching experiment followed a standard BCR four-step procedure, while selective leaching involved seven different chemical extractants. Results and discussion: The results from selective and sequential leaching methods are consistent. In general, very little of the heavy metals were found in the easily soluble or exchangeable fractions. Larger fractions of Cd and Zn can be leached out than other metals. Lead appears predominantly in the organic or carbonate fractions, of which {proportional_to} 30-60% is in the easily soluble organic fraction. Most As cannot be leached out by any of the extractants used, but it could have been complicated by the ineffective dissolution of oxides by ammonium hydroxylamine. Ni and Cr were mostly in the residual fractions but some released in the oxidizable fractions. Therefore, the leachability of metals follow the order Cd/Zn > Pb > Ni/Cr. Conclusions: Despite of the controversy and inaccuracy surrounding chemical leaching methods for the speciation of metals, chemical leaching data provide important, general, and easy-to-access information on the mobility of heavy metals

Modified sequential extraction for biochar and petroleum coke: Metal release potential and its environmental implications.

Science.gov (United States)

von Gunten, Konstantin; Alam, Md Samrat; Hubmann, Magdalena; Ok, Yong Sik; Konhauser, Kurt O; Alessi, Daniel S

2017-07-01

A modified Community Bureau of Reference (CBR) sequential extraction method was tested to assess the composition of untreated pyrogenic carbon (biochar) and oil sands petroleum coke. Wood biochar samples were found to contain lower concentrations of metals, but had higher fractions of easily mobilized alkaline earth and transition metals. Sewage sludge biochar was determined to be less recalcitrant and had higher total metal concentrations, with most of the metals found in the more resilient extraction fractions (oxidizable, residual). Petroleum coke was the most stable material, with a similar metal distribution pattern as the sewage sludge biochar. The applied sequential extraction method represents a suitable technique to recover metals from these materials, and is a valuable tool in understanding the metal retaining and leaching capability of various biochar types and carbonaceous petroleum coke samples. Copyright © 2017 Elsevier Ltd. All rights reserved.

Conformable Fractional Bessel Equation and Bessel Functions

OpenAIRE

Gökdoğan, Ahmet; Ünal, Emrah; Çelik, Ercan

2015-01-01

In this work, we study the fractional power series solutions around regular singular point x=0 of conformable fractional Bessel differential equation and fractional Bessel functions. Then, we compare fractional solutions with ordinary solutions. In addition, we present certain property of fractional Bessel functions.

A method based on the Jacobi tau approximation for solving multi-term time-space fractional partial differential equations

Science.gov (United States)

Bhrawy, A. H.; Zaky, M. A.

2015-01-01

In this paper, we propose and analyze an efficient operational formulation of spectral tau method for multi-term time-space fractional differential equation with Dirichlet boundary conditions. The shifted Jacobi operational matrices of Riemann-Liouville fractional integral, left-sided and right-sided Caputo fractional derivatives are presented. By using these operational matrices, we propose a shifted Jacobi tau method for both temporal and spatial discretizations, which allows us to present an efficient spectral method for solving such problem. Furthermore, the error is estimated and the proposed method has reasonable convergence rates in spatial and temporal discretizations. In addition, some known spectral tau approximations can be derived as special cases from our algorithm if we suitably choose the corresponding special cases of Jacobi parameters θ and ϑ. Finally, in order to demonstrate its accuracy, we compare our method with those reported in the literature.

Fractionation of 137Cs and Pu in natural peatland

International Nuclear Information System (INIS)

Mihalík, Ján; Bartusková, Miluše; Hölgye, Zoltán; Ježková, Tereza; Henych, Ondřej

2014-01-01

High Cs-137 concentrations in plants growing on peatland inspired us to investigate the quantity of its bioavailable fraction in natural peat. Our investigation aims to: a) estimate the quantity of bioavailable Cs-137 and Pu present in peat, b) verify the similarity of Cs-137 and K-40 behaviours, and c) perform a quantification of Cs-137 and Pu transfer from peat to plants. We analysed the vertical distribution of Cs-137 and Pu isotopes in the peat and their concentrations in plants growing on these places. Bioavailability of radionuclides was investigated by sequential extraction. Sequential analyses revealed that it was the upper layer which contained the majority of Cs-137 in an available form while deeper layers retained Cs-137 in immobile fractions. We can conclude that 18% of all Cs-137 in the peat is still bioavailable. Despite of the low quantity of bioavailable fraction of Cs-137 its transfer factor reached extremely high values. In the case of Pu, 64% of its total amount was associated with fulvic/humic acids which resulted in the high transfer factor from peat to plants. 27 years after the Chernobyl nuclear accident, the significant part of radionuclides deposited in peatland is still bioavailable. - Highlights: • Decrease of exchangeable 137 Cs and its increase in residual fraction with depth. • High 137 Cs transfer factor contrary to its low quantity in bioavailable fractions. • Fulvic/humic acids are a more effective carrier for Pu than for Cs

Characterization and blood coagulation evaluation of the water-soluble chitooligosaccharides prepared by a facile fractionation method.

Science.gov (United States)

Lin, Chia-Wen; Lin, Jui-Che

2003-01-01

Water-soluble chitooligosaccharides have been reported to have specific biological activities. In this study, the chitosan samples with different degree of acetylation were used separately to prepare chitooligosaccharide (COS) and highly deacetylated chitooligosaccharide (HDCOS) through the nitrous acid depolymerization. Rather than using the conventional fractionation schemes commonly employed, such as dialysis and ultrafiltration which require a large amount of deionized water as well as a fair long dwell time, an unique fractionation scheme is explored to recover and desalt these nitrous-acid depolymerized chitosan with different molecular weights. This fractionation scheme is based on the differential solubility variation of depolymerized products within the aqueous solutions that contain various ratios of methanol. It was noted that chitosan with different molecular weight can be successfully recovered and fractionated with methanol added sequentially up to a volume of four times of original depolmerized product. In addition, chemical characterization of the fractionated water-soluble COS and HDCOS by 1H NMR spectroscopy and diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS) indicated that the chitosan depolymerization reaction is greatly influenced by the degree of acetylation of the parental chitosan reactant. Moreover, the modified whole blood clotting time assay and the platelet coagulation test suggested that the 1:2 fractionated water-soluble COS and HDCOS obtained are much less procoagulant than their parental chitosan compound and can be of use in biomedical applications in which blood coagulation is not desired.

Dynamic Prediction of Power Storage and Delivery by Data-Based Fractional Differential Models of a Lithium Iron Phosphate Battery

Directory of Open Access Journals (Sweden)

Yunfeng Jiang

2016-07-01

Full Text Available A fractional derivative system identification approach for modeling battery dynamics is presented in this paper, where fractional derivatives are applied to approximate non-linear dynamic behavior of a battery system. The least squares-based state-variable filter (LSSVF method commonly used in the identification of continuous-time models is extended to allow the estimation of fractional derivative coefficents and parameters of the battery models by monitoring a charge/discharge demand signal and a power storage/delivery signal. In particular, the model is combined by individual fractional differential models (FDMs, where the parameters can be estimated by a least-squares algorithm. Based on experimental data, it is illustrated how the fractional derivative model can be utilized to predict the dynamics of the energy storage and delivery of a lithium iron phosphate battery (LiFePO 4 in real-time. The results indicate that a FDM can accurately capture the dynamics of the energy storage and delivery of the battery over a large operating range of the battery. It is also shown that the fractional derivative model exhibits improvements on prediction performance compared to standard integer derivative model, which in beneficial for a battery management system.

Angular analysis and differential branching fraction of the decay B{sub s}{sup 0}→ϕμ{sup +}μ{sup −}

Energy Technology Data Exchange (ETDEWEB)

Aaij, R. [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Adeva, B. [Universidad de Santiago de Compostela, Santiago de Compostela (Spain); Adinolfi, M. [H.H. Wills Physics Laboratory, University of Bristol, Bristol (United Kingdom); Affolder, A. [Oliver Lodge Laboratory, University of Liverpool, Liverpool (United Kingdom); Collaboration: The LHCb collaboration; and others

2015-09-25

An angular analysis and a measurement of the differential branching fraction of the decay B{sub s}{sup 0}→ϕμ{sup +}μ{sup −} are presented, using data corresponding to an integrated luminosity of 3.0 fb{sup −1} of pp collisions recorded by the LHCb experiment at √s=7 and 8 TeV. Measurements are reported as a function of q{sup 2}, the square of the dimuon invariant mass and results of the angular analysis are found to be consistent with the Standard Model. In the range 1differential branching fraction is found to be more than 3 σ below the Standard Model predictions.

A Note on a Semilinear Fractional Differential Equation of Neutral Type with Infinite Delay

Directory of Open Access Journals (Sweden)

Gisle M. Mophou

2010-01-01

Full Text Available We deal in this paper with the mild solution for the semilinear fractional differential equation of neutral type with infinite delay: Dαx(t+Ax(t=f(t,xt, t∈[0,T], x(t=ϕ(t, t∈]−∞,0], with T>0 and 0<α<1. We prove the existence (and uniqueness of solutions, assuming that −A is a linear closed operator which generates an analytic semigroup (T(tt≥0 on a Banach space 𝕏 by means of the Banach's fixed point theorem. This generalizes some recent results.

Selective solubilization of membrane proteins differentially labeled by p-chloromercuribenzenesulfonic acid in the presence of sucrose

International Nuclear Information System (INIS)

M'Batchi, B.; Pichelin, D.; Delrot, S.

1987-01-01

Broadbean (Vicia faba L.) leaf discs have been incubated with the slowly permeant thiol reagent [ 203 Hg]-para-chloromercuribenzenesulfonic acid (PCMBS) in the presence or in the absence of sucrose, and the release of PCMBS-labeled proteins has been monitored in media containing various concentrations of urea, ethylene glycol-bis-(β-aminoethyl ether)-N, N, N', N'-tetraacetic acid (EGTA), sodium cholate, sodium dodecyl sulfate, Triton X-100, octylglucoside or (3-[3-cholamidopropyl)-dimethylammonio] 1-propane-sulfonate)(CHAPS). The proteins differentially labeled by PCMBS in the presence of sucrose which, on the basis of previous results, are assumed to included the sucrose carrier, were preferentially solubilized by 1% CHAPS, 1% octylglucoside, or 1% Triton X-100. Other PCMBS-labeled proteins (background proteins) could be partially removed by EGTA, urea, or 0.1% cholate. Sequential treatment by 10 mM EGTA and 1% CHAPS was found to give a fraction highly enriched in the differentially labeled proteins. Analysis of the specific activity of microsomal pellets suggests that the results obtained with leaf discs give a good account of what is occurring at the plasma membrane level. These data, which suggest that the proteins differentially labeled, by PCMBS in the presence of sucrose are intrinsic membrane proteins, can be used to solubilize these proteins from microsomal fractions

Sequential stenotic strictures of the small bowel leading to obstruction

Institute of Scientific and Technical Information of China (English)

无

2007-01-01

Small bowel obstructions (SBOs) are primarily caused by adhesions, hernias, neoplasms, or inflammatory strictures. Intraluminal strictures are an uncommon cause of SBO. This report describes our findings in a unique case of sequential, stenotic intraluminal strictures of the small intestine, discusses the differential diagnosis of intraluminal intestinal strictures, and reviews the literature regarding intraluminal pathology.

A fractional spline collocation-Galerkin method for the time-fractional diffusion equation

Directory of Open Access Journals (Sweden)

Pezza L.

2018-03-01

Full Text Available The aim of this paper is to numerically solve a diffusion differential problem having time derivative of fractional order. To this end we propose a collocation-Galerkin method that uses the fractional splines as approximating functions. The main advantage is in that the derivatives of integer and fractional order of the fractional splines can be expressed in a closed form that involves just the generalized finite difference operator. This allows us to construct an accurate and efficient numerical method. Several numerical tests showing the effectiveness of the proposed method are presented.

The Fractional Orthogonal Difference with Applications

Directory of Open Access Journals (Sweden)

Enno Diekema

2015-06-01

Full Text Available This paper is a follow-up of a previous paper of the author published in Mathematics journal in 2015, which treats the so-called continuous fractional orthogonal derivative. In this paper, we treat the discrete case using the fractional orthogonal difference. The theory is illustrated with an application of a fractional differentiating filter. In particular, graphs are presented of the absolutel value of the modulus of the frequency response. These make clear that for a good insight into the behavior of a fractional differentiating filter, one has to look for the modulus of its frequency response in a log-log plot, rather than for plots in the time domain.

Differential proteomic analysis reveals sequential heat stress-responsive regulatory network in radish (Raphanus sativus L.) taproot.

Science.gov (United States)

Wang, Ronghua; Mei, Yi; Xu, Liang; Zhu, Xianwen; Wang, Yan; Guo, Jun; Liu, Liwang

2018-05-01

Differential abundance protein species (DAPS) involved in reducing damage and enhancing thermotolerance in radish were firstly identified. Proteomic analysis and omics association analysis revealed a HS-responsive regulatory network in radish. Heat stress (HS) is a major destructive factor influencing radish production and supply in summer, for radish is a cool season vegetable crop being susceptible to high temperature. In this study, the proteome changes of radish taproots under 40 °C treatment at 0 h (Control), 12 h (Heat12) and 24 h (Heat24) were analyzed using iTRAQ (Isobaric Tag for Relative and Absolute Quantification) approach. In total, 2258 DAPS representing 1542 differentially accumulated uniprotein species which respond to HS were identified. A total of 604, 910 and 744 DAPS was detected in comparison of Control vs. Heat12, Control vs. Heat24, and Heat12 vs. Heat24, respectively. Gene ontology and pathway analysis showed that annexin, ubiquitin-conjugating enzyme, ATP synthase, heat shock protein (HSP) and other stress-related proteins were predominately enriched in signal transduction, stress and defense pathways, photosynthesis and energy metabolic pathways, working cooperatively to reduce stress-induced damage in radish. Based on iTRAQ combined with the transcriptomics analysis, a schematic model of a sequential HS-responsive regulatory network was proposed. The initial sensing of HS occurred at the plasma membrane, and then key components of stress signal transduction triggered heat-responsive genes in the plant protective metabolism to re-establish homeostasis and enhance thermotolerance. These results provide new insights into characteristics of HS-responsive DAPS and facilitate dissecting the molecular mechanisms underlying heat tolerance in radish and other root crops.

Application of the enhanced homotopy perturbation method to solve the fractional-order Bagley-Torvik differential equation

Energy Technology Data Exchange (ETDEWEB)

Zolfaghari, M; Ghaderi, R; Sheikhol Eslami, A; Hosseinnia, S H; Sadati, J [Intelligent System Research Group, Faculty of Electrical and Computer Engineering, Babol, Noushirvani University of Technology, PO Box 47135-484, Babol (Iran, Islamic Republic of); Ranjbar, A [Golestan University, Gorgan (Iran, Islamic Republic of); Momani, S [Department of Mathematics, Mutah University, PO Box 7, Al-Karak (Jordan)], E-mail: h.hoseinnia@stu.nit.ac.ir, E-mail: a.ranjbar@nit.ac.ir, E-mail: shahermm@yahoo.com

2009-10-15

The enhanced homotopy perturbation method (EHPM) is applied for finding improved approximate solutions of the well-known Bagley-Torvik equation for three different cases. The main characteristic of the EHPM is using a stabilized linear part, which guarantees the stability and convergence of the overall solution. The results are finally compared with the Adams-Bashforth-Moulton numerical method, the Adomian decomposition method (ADM) and the fractional differential transform method (FDTM) to verify the performance of the EHPM.

Application of the enhanced homotopy perturbation method to solve the fractional-order Bagley-Torvik differential equation

International Nuclear Information System (INIS)

Zolfaghari, M; Ghaderi, R; Sheikhol Eslami, A; Hosseinnia, S H; Sadati, J; Ranjbar, A; Momani, S

2009-01-01

The enhanced homotopy perturbation method (EHPM) is applied for finding improved approximate solutions of the well-known Bagley-Torvik equation for three different cases. The main characteristic of the EHPM is using a stabilized linear part, which guarantees the stability and convergence of the overall solution. The results are finally compared with the Adams-Bashforth-Moulton numerical method, the Adomian decomposition method (ADM) and the fractional differential transform method (FDTM) to verify the performance of the EHPM.

Application of the enhanced homotopy perturbation method to solve the fractional-order Bagley-Torvik differential equation

Science.gov (United States)

Zolfaghari, M.; Ghaderi, R.; Sheikhol Eslami, A.; Ranjbar, A.; Hosseinnia, S. H.; Momani, S.; Sadati, J.

2009-10-01

The enhanced homotopy perturbation method (EHPM) is applied for finding improved approximate solutions of the well-known Bagley-Torvik equation for three different cases. The main characteristic of the EHPM is using a stabilized linear part, which guarantees the stability and convergence of the overall solution. The results are finally compared with the Adams-Bashforth-Moulton numerical method, the Adomian decomposition method (ADM) and the fractional differential transform method (FDTM) to verify the performance of the EHPM.

Group formalism of Lie transformations to time-fractional partial ...

Indian Academy of Sciences (India)

Lie symmetry analysis; Fractional partial differential equation; Riemann–Liouville fractional derivative ... science and engineering. It is known that while ... differential equations occurring in different areas of applied science [11,14]. The Lie ...

Utilizing a sequential injection system furnished with an extraction microcolumn as a novel approach for executing sequential extractions of metal species in solid samples

DEFF Research Database (Denmark)

Chomchoei, R.; Hansen, Elo Harald; Shiowatana, J.

2007-01-01

This communication presents a novel approach to perform sequential extraction of elements in solid samples by using a sequential injection (SI) system incorporating a specially designed extraction microcolumn. Based on the operation of the syringe pump, different modes of extraction are potentially...... that the system entails many advantages such as being fully automated, and besides being characterised by rapidity, ease of operation and robustness, it is less prone to risks of contamination and personal errors as encountered in traditional batch systems. Moreover, improvement of the precision and accuracy...... of the chemical fractionation of metal in solids as compared with previous reports are obtained. The system ensures that extraction is performed at designated pH values. Variation of sample weight to column volume ratios do not affect the amounts of extractable metals, nor do extraction flow rates ranging from 50...

Existence of positive solutions for multi-term non-autonomous fractional differential equations with polynomial coefficients

Directory of Open Access Journals (Sweden)

Azizollah Babakhani

2006-10-01

Full Text Available In the present paper we discuss the existence of positive solutions in the case of multi-term non-autonomous fractional differential equations with polynomial coefficients; the constant coefficient case has been studied in [2]. We consider the equation $$ Big(D^{alpha_n} -sum_{j = 1}^{n - 1} p_j(xD^{alpha_{n - j}}Bigy = f(x, y. $$ We state various conditions on $f$ and $p_j$'s under which this equation has: positive solutions, a unique solution which is positive, and a unique solution which may not be positive.

Measurements of the S-wave fraction in B{sup 0}→K{sup +}π{sup −}μ{sup +}μ{sup −} decays and the B{sup 0}→K{sup ∗}(892){sup 0}μ{sup +}μ{sup −} differential branching fraction

Energy Technology Data Exchange (ETDEWEB)

Aaij, R. [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Adeva, B. [Universidad de Santiago de Compostela, Santiago de Compostela (Spain); Adinolfi, M. [H.H. Wills Physics Laboratory, University of Bristol, Bristol (United Kingdom); Ajaltouni, Z. [Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-Ferrand (France); Collaboration: The LHCb collaboration; and others

2016-11-08

A measurement of the differential branching fraction of the decay B{sup 0}→K{sup ∗}(892){sup 0}μ{sup +}μ{sup −} is presented together with a determination of the S-wave fraction of the K{sup +}π{sup −} system in the decay B{sup 0}→K{sup +}π{sup −}μ{sup +}μ{sup −}. The analysis is based on pp-collision data corresponding to an integrated luminosity of 3 fb{sup −1} collected with the LHCb experiment. The measurements are made in bins of the invariant mass squared of the dimuon system, q{sup 2}. Precise theoretical predictions for the differential branching fraction of B{sup 0}→K{sup ∗}(892){sup 0}μ{sup +}μ{sup −} decays are available for the q{sup 2} region 1.1fraction of the K{sup +}π{sup −} system in B{sup 0}→K{sup +}π{sup −}μ{sup +}μ{sup −} decays is found to be F{sub S}=0.101±0.017(stat)±0.009(syst), and the differential branching fraction of B{sup 0}→K{sup ∗}(892){sup 0}μ{sup +}μ{sup −} decays is determined to be dB/dq{sup 2}=(0.392 {sub −0.019} {sup +0.020}(stat)±0.010(syst)±0.027(norm))×10{sup −7}c{sup 4}/GeV{sup 2}. The differential branching fraction measurements presented are the most precise to date and are found to be in agreement with Standard Model predictions.

-Dimensional Fractional Lagrange's Inversion Theorem

Directory of Open Access Journals (Sweden)

F. A. Abd El-Salam

2013-01-01

Full Text Available Using Riemann-Liouville fractional differential operator, a fractional extension of the Lagrange inversion theorem and related formulas are developed. The required basic definitions, lemmas, and theorems in the fractional calculus are presented. A fractional form of Lagrange's expansion for one implicitly defined independent variable is obtained. Then, a fractional version of Lagrange's expansion in more than one unknown function is generalized. For extending the treatment in higher dimensions, some relevant vectors and tensors definitions and notations are presented. A fractional Taylor expansion of a function of -dimensional polyadics is derived. A fractional -dimensional Lagrange inversion theorem is proved.

Availability and bio-accessibility of metals in the clay fraction of urban soils of Sevilla

International Nuclear Information System (INIS)

Madrid, F.; Diaz-Barrientos, E.; Madrid, L.

2008-01-01

The availability of Cd, Cr, Cu, Ni, Mn, Pb and Zn present in the finest size particles of urban soils is studied by comparing the concentrations in the clay fraction with those extracted from the whole soil by either single-extraction or sequential extraction method. Many metals are preferentially present in the finest particles as compared to coarser fractions. This is true for most metals studied, except Mn and, perhaps, Cd. Those metals present in the clay fraction are often in easily bio-accessible forms, especially Cu, Pb and Zn. The results suggest that bio-accessible forms of these three metals are distributed among the three sequential fractions, and even the fraction considered as 'residual' is also bio-accessible to a significant extent. The statistical analysis shows some distinctions among metals that are compared to the 'urban', 'natural', or intermediate behaviour of the various metals as proposed earlier in the literature. - The recreational use of most urban soils causes that the availability of metals in the finest soil particles must be studied and eventually controlled

Local Fractional Adomian Decomposition and Function Decomposition Methods for Laplace Equation within Local Fractional Operators

Directory of Open Access Journals (Sweden)

Sheng-Ping Yan

2014-01-01

Full Text Available We perform a comparison between the local fractional Adomian decomposition and local fractional function decomposition methods applied to the Laplace equation. The operators are taken in the local sense. The results illustrate the significant features of the two methods which are both very effective and straightforward for solving the differential equations with local fractional derivative.

Sequential Detection of Thermophilic Lipase and Protease by Zymography.

Science.gov (United States)

Kurz, Liliana; Hernández, Zully; Contreras, Lellys M; Wilkesman, Jeff

2017-01-01

Lipase and protease present in cell-free fractions of thermophilic Bacillus sp. cultures were analyzed by polyacrylamide gel (PAG) electrophoresis. After run, the gel is electrotransferred to another PAG copolymerized with glycerol tributyrate, olive oil, and gelatin. This multi-substrate gel was incubated first for lipase detection, until bands appeared, and then stained with Coomassie for protease detection. Advantages of this sequential procedure are the detection of two different enzyme activities on a single PAG, beside time and resource saving.

Discrete fractional solutions of a Legendre equation

Science.gov (United States)

Yılmazer, Resat

2018-01-01

One of the most popular research interests of science and engineering is the fractional calculus theory in recent times. Discrete fractional calculus has also an important position in fractional calculus. In this work, we acquire new discrete fractional solutions of the homogeneous and non homogeneous Legendre differential equation by using discrete fractional nabla operator.

On the fractional Eulerian numbers and equivalence of maps with long term power-law memory (integral Volterra equations of the second kind) to Grünvald-Letnikov fractional difference (differential) equations.

Science.gov (United States)

Edelman, Mark

2015-07-01

In this paper, we consider a simple general form of a deterministic system with power-law memory whose state can be described by one variable and evolution by a generating function. A new value of the system's variable is a total (a convolution) of the generating functions of all previous values of the variable with weights, which are powers of the time passed. In discrete cases, these systems can be described by difference equations in which a fractional difference on the left hand side is equal to a total (also a convolution) of the generating functions of all previous values of the system's variable with the fractional Eulerian number weights on the right hand side. In the continuous limit, the considered systems can be described by the Grünvald-Letnikov fractional differential equations, which are equivalent to the Volterra integral equations of the second kind. New properties of the fractional Eulerian numbers and possible applications of the results are discussed.

The mental representations of fractions: adults' same–different judgments

Science.gov (United States)

Gabriel, Florence; Szucs, Denes; Content, Alain

2013-01-01

Two experiments examined whether the processing of the magnitude of fractions is global or componential. Previously, some authors concluded that adults process the numerators and denominators of fractions separately and do not access the global magnitude of fractions. Conversely, others reported evidence suggesting that the global magnitude of fractions is accessed. We hypothesized that in a fraction matching task, participants automatically extract the magnitude of the components but that the activation of the global magnitude of the whole fraction is only optional or strategic. Participants carried out same/different judgment tasks. Two different tasks were used: a physical matching task and a numerical matching task. Pairs of fractions were presented either simultaneously or sequentially. Results showed that participants only accessed the representation of the global magnitude of fractions in the numerical matching task. The mode of stimulus presentation did not affect the processing of fractions. The present study allows a deeper understanding of the conditions in which the magnitude of fractions is mentally represented by using matching tasks and two different modes of presentation. PMID:23847562

Lead isotopes combined with a sequential extraction procedure for source apportionment in the dry deposition of Asian dust and non-Asian dust

International Nuclear Information System (INIS)

Lee, Pyeong-Koo; Yu, Soonyoung

2016-01-01

Lead isotopic compositions were determined in leachates that were generated using sequential extractions of dry deposition samples of Asian dust (AD) and non-Asian dust (NAD) and Chinese desert soils, and used to apportion Pb sources. Results showed significant differences in "2"0"6Pb/"2"0"7Pb and "2"0"6Pb/"2"0"4Pb isotopic compositions in non-residual fractions between the dry deposition samples and the Chinese desert soils while "2"0"6Pb/"2"0"7Pb and "2"0"6Pb/"2"0"4Pb isotopic compositions in residual fraction of the dry deposition of AD and NAD were similar to the mean "2"0"6Pb/"2"0"7Pb and "2"0"6Pb/"2"0"4Pb in residual fraction of the Alashan Plateau soil. These results indicate that the geogenic materials of the dry deposition of AD and NAD were largely influenced by the Alashan Plateau soil, while the secondary sources of the dry deposition were different from those of the Chinese desert soils. In particular, the lead isotopic compositions in non-residual fractions of the dry deposition were homogenous, which implies that the non-residual four fractions (F1 to F4) shared the primary anthropogenic origin. "2"0"6Pb/"2"0"7Pb values and the predominant wind directions in the study area suggested that airborne particulates of heavily industrialized Chinese cities were one of the main Pb sources. Source apportionment calculations showed that the average proportion of anthropogenic Pb in the dry deposition of AD and NAD was 87% and 95% respectively in total Pb extraction, 92% and 97% in non-residual fractions, 15% and 49% in residual fraction. Approximately 81% and 80% of the anthropogenic Pb was contributed by coal combustion in China in the dry deposition of AD and NAD respectively while the remainder was derived from industrial Pb contamination. The research result proposes that sequential extractions with Pb isotope analysis are a useful tool for the discrimination of anthropogenic and geogenic origins in highly contaminated AD and NAD. - Highlights: �

The Positive Properties of Green’s Function for Fractional Differential Equations and Its Applications

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Fuquan Jiang

2013-01-01

Full Text Available We consider the properties of Green’s function for the nonlinear fractional differential equation boundary value problem: D0+αu(t+f(t,u(t+e(t=0,0

Differential branching fraction and angular anaysis of Λb→Λμ+μ− decays

CERN Multimedia

Pescatore, Luca

2015-01-01

The differential branching fraction of the rare decay Λ0b → Λμ+μ− is measured as a function of q2, the square of the dimuon invariant mass. The analysis is performed using data collected by the LHCb experiment, corresponding to an integrated luminosity of 3.0 fb−1. These include evidence for signal at dimuon masses below the square of the J/ψ mass with significance above 3σ. In the q2 intervals where the signal is observed, angular distributions are studied and the forward-backward asymmetries in the dimuon and hadron systems are measured for the first time.

Similarity Solutions for Multiterm Time-Fractional Diffusion Equation

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A. Elsaid

2016-01-01

Full Text Available Similarity method is employed to solve multiterm time-fractional diffusion equation. The orders of the fractional derivatives belong to the interval (0,1] and are defined in the Caputo sense. We illustrate how the problem is reduced from a multiterm two-variable fractional partial differential equation to a multiterm ordinary fractional differential equation. Power series solution is obtained for the resulting ordinary problem and the convergence of the series solution is discussed. Based on the obtained results, we propose a definition for a multiterm error function with generalized coefficients.

Wavelet Methods for Solving Fractional Order Differential Equations

OpenAIRE

A. K. Gupta; S. Saha Ray

2014-01-01

Fractional calculus is a field of applied mathematics which deals with derivatives and integrals of arbitrary orders. The fractional calculus has gained considerable importance during the past decades mainly due to its application in diverse fields of science and engineering such as viscoelasticity, diffusion of biological population, signal processing, electromagnetism, fluid mechanics, electrochemistry, and many more. In this paper, we review different wavelet methods for solving both linea...

Fractional model for heat conduction in polar bear hairs

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Wang Qing-Li

2012-01-01

Full Text Available Time-fractional differential equations can accurately describe heat conduction in fractal media, such as wool fibers, goose down and polar bear hair. The fractional complex transform is used to convert time-fractional heat conduction equations with the modified Riemann-Liouville derivative into ordinary differential equations, and exact solutions can be easily obtained. The solution process is straightforward and concise.

Efficient Galerkin solution of stochastic fractional differential equations using second kind Chebyshev wavelets

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Fakhrodin Mohammadi

2017-10-01

Full Text Available ‎Stochastic fractional differential equations (SFDEs have been used for modeling many physical problems in the fields of turbulance‎, ‎heterogeneous‎, ‎flows and matrials‎, ‎viscoelasticity and electromagnetic theory‎. ‎In this paper‎, ‎an‎ efficient wavelet Galerkin method based on the second kind Chebyshev wavelets are proposed for approximate solution of SFDEs‎. ‎In ‎this ‎app‎roach‎‎, ‎o‎perational matrices of the second kind Chebyshev wavelets ‎are used ‎for reducing SFDEs to a linear system of algebraic equations that can be solved easily‎. ‎C‎onvergence and error analysis of the proposed method is ‎considered‎.‎ ‎Some numerical examples are performed to confirm the applicability and efficiency of the proposed method‎.

Sequential and simultaneous strategies for biorefining of wheat straw using room temperature ionic liquids, xylanases and cellulases.

Science.gov (United States)

Husson, Eric; Auxenfans, Thomas; Herbaut, Mickael; Baralle, Manon; Lambertyn, Virginie; Rakotoarivonina, Harivoni; Rémond, Caroline; Sarazin, Catherine

2018-03-01

Sequential and simultaneous strategies for fractioning wheat straw were developed in combining 1-ethyl-3-methyl imidazolium acetate [C2mim][OAc], endo-xylanases from Thermobacillus xylanilyticus and commercial cellulases. After [C2mim][OAc]-pretreatment, hydrolysis catalyzed by endo-xylanases of wheat straw led to efficient xylose production with very competitive yield (97.6 ± 1.3%). Subsequent enzymatic saccharification allowed achieving a total degradation of cellulosic fraction (>99%). These high performances revealed an interesting complementarity of [C2mim][OAc]- and xylanase-pretreatments for increasing enzymatic digestibility of cellulosic fraction in agreement with the structural and morphological changes of wheat straw induced by each of these pretreatment steps. In addition a higher tolerance of endo-xylanases from T. xylaniliticus to [C2mim][AcO] until 30% v/v than cellulases from T. reesei was observed. Based on this property, a simultaneous strategy combining [C2mim][OAc]- and endo-xylanases as pretreatment in a one-batch produced xylose with similar yield than those obtained by the sequential strategy. Copyright © 2017 Elsevier Ltd. All rights reserved.

Statistical analysis of dose heterogeneity in circulating blood: Implications for sequential methods of total body irradiation

International Nuclear Information System (INIS)

Molloy, Janelle A.

2010-01-01

Purpose: Improvements in delivery techniques for total body irradiation (TBI) using Tomotherapy and intensity modulated radiation therapy have been proven feasible. Despite the promise of improved dose conformality, the application of these ''sequential'' techniques has been hampered by concerns over dose heterogeneity to circulating blood. The present study was conducted to provide quantitative evidence regarding the potential clinical impact of this heterogeneity. Methods: Blood perfusion was modeled analytically as possessing linear, sinusoidal motion in the craniocaudal dimension. The average perfusion period for human circulation was estimated to be approximately 78 s. Sequential treatment delivery was modeled as a Gaussian-shaped dose cloud with a 10 cm length that traversed a 183 cm patient length at a uniform speed. Total dose to circulating blood voxels was calculated via numerical integration and normalized to 2 Gy per fraction. Dose statistics and equivalent uniform dose (EUD) were calculated for relevant treatment times, radiobiological parameters, blood perfusion rates, and fractionation schemes. The model was then refined to account for random dispersion superimposed onto the underlying periodic blood flow. Finally, a fully stochastic model was developed using binomial and trinomial probability distributions. These models allowed for the analysis of nonlinear sequential treatment modalities and treatment designs that incorporate deliberate organ sparing. Results: The dose received by individual blood voxels exhibited asymmetric behavior that depended on the coherence among the blood velocity, circulation phase, and the spatiotemporal characteristics of the irradiation beam. Heterogeneity increased with the perfusion period and decreased with the treatment time. Notwithstanding, heterogeneity was less than ±10% for perfusion periods less than 150 s. The EUD was compromised for radiosensitive cells, long perfusion periods, and short treatment times

Statistical analysis of dose heterogeneity in circulating blood: implications for sequential methods of total body irradiation.

Science.gov (United States)

Molloy, Janelle A

2010-11-01

Improvements in delivery techniques for total body irradiation (TBI) using Tomotherapy and intensity modulated radiation therapy have been proven feasible. Despite the promise of improved dose conformality, the application of these "sequential" techniques has been hampered by concerns over dose heterogeneity to circulating blood. The present study was conducted to provide quantitative evidence regarding the potential clinical impact of this heterogeneity. Blood perfusion was modeled analytically as possessing linear, sinusoidal motion in the craniocaudal dimension. The average perfusion period for human circulation was estimated to be approximately 78 s. Sequential treatment delivery was modeled as a Gaussian-shaped dose cloud with a 10 cm length that traversed a 183 cm patient length at a uniform speed. Total dose to circulating blood voxels was calculated via numerical integration and normalized to 2 Gy per fraction. Dose statistics and equivalent uniform dose (EUD) were calculated for relevant treatment times, radiobiological parameters, blood perfusion rates, and fractionation schemes. The model was then refined to account for random dispersion superimposed onto the underlying periodic blood flow. Finally, a fully stochastic model was developed using binomial and trinomial probability distributions. These models allowed for the analysis of nonlinear sequential treatment modalities and treatment designs that incorporate deliberate organ sparing. The dose received by individual blood voxels exhibited asymmetric behavior that depended on the coherence among the blood velocity, circulation phase, and the spatiotemporal characteristics of the irradiation beam. Heterogeneity increased with the perfusion period and decreased with the treatment time. Notwithstanding, heterogeneity was less than +/- 10% for perfusion periods less than 150 s. The EUD was compromised for radiosensitive cells, long perfusion periods, and short treatment times. However, the EUD was

Fractionation of (137)Cs and Pu in natural peatland.

Science.gov (United States)

Mihalík, Ján; Bartusková, Miluše; Hölgye, Zoltán; Ježková, Tereza; Henych, Ondřej

2014-08-01

High Cs-137 concentrations in plants growing on peatland inspired us to investigate the quantity of its bioavailable fraction in natural peat. Our investigation aims to: a) estimate the quantity of bioavailable Cs-137 and Pu present in peat, b) verify the similarity of Cs-137 and K-40 behaviours, and c) perform a quantification of Cs-137 and Pu transfer from peat to plants. We analysed the vertical distribution of Cs-137 and Pu isotopes in the peat and their concentrations in plants growing on these places. Bioavailability of radionuclides was investigated by sequential extraction. Sequential analyses revealed that it was the upper layer which contained the majority of Cs-137 in an available form while deeper layers retained Cs-137 in immobile fractions. We can conclude that 18% of all Cs-137 in the peat is still bioavailable. Despite of the low quantity of bioavailable fraction of Cs-137 its transfer factor reached extremely high values. In the case of Pu, 64% of its total amount was associated with fulvic/humic acids which resulted in the high transfer factor from peat to plants. 27 years after the Chernobyl nuclear accident, the significant part of radionuclides deposited in peatland is still bioavailable. Copyright © 2014 Elsevier Ltd. All rights reserved.

Sequential Power-Dependence Theory

NARCIS (Netherlands)

Buskens, Vincent; Rijt, Arnout van de

2008-01-01

Existing methods for predicting resource divisions in laboratory exchange networks do not take into account the sequential nature of the experimental setting. We extend network exchange theory by considering sequential exchange. We prove that Sequential Power-Dependence Theory—unlike

Numerical analysis for the fractional diffusion and fractional Buckmaster equation by the two-step Laplace Adam-Bashforth method

Science.gov (United States)

Jain, Sonal

2018-01-01

In this paper, we aim to use the alternative numerical scheme given by Gnitchogna and Atangana for solving partial differential equations with integer and non-integer differential operators. We applied this method to fractional diffusion model and fractional Buckmaster models with non-local fading memory. The method yields a powerful numerical algorithm for fractional order derivative to implement. Also we present in detail the stability analysis of the numerical method for solving the diffusion equation. This proof shows that this method is very stable and also converges very quickly to exact solution and finally some numerical simulation is presented.

Exact solutions of fractional mBBM equation and coupled system of fractional Boussinesq-Burgers

Science.gov (United States)

Javeed, Shumaila; Saif, Summaya; Waheed, Asif; Baleanu, Dumitru

2018-06-01

The new exact solutions of nonlinear fractional partial differential equations (FPDEs) are established by adopting first integral method (FIM). The Riemann-Liouville (R-L) derivative and the local conformable derivative definitions are used to deal with the fractional order derivatives. The proposed method is applied to get exact solutions for space-time fractional modified Benjamin-Bona-Mahony (mBBM) equation and coupled time-fractional Boussinesq-Burgers equation. The suggested technique is easily applicable and effectual which can be implemented successfully to obtain the solutions for different types of nonlinear FPDEs.

An extended integrable fractional-order KP soliton hierarchy

International Nuclear Information System (INIS)

Li Li

2011-01-01

In this Letter, we consider the modified derivatives and integrals of fractional-order pseudo-differential operators. A sequence of Lax KP equations hierarchy and extended fractional KP (fKP) hierarchy are introduced, and the fKP hierarchy has Lax presentations with the extended Lax operators. In the case of the extension with the half-order pseudo-differential operators, a new integrable fKP hierarchy is obtained. A few particular examples of fractional order will be listed, together with their Lax pairs.

An extended integrable fractional-order KP soliton hierarchy

Energy Technology Data Exchange (ETDEWEB)

Li Li, E-mail: li07099@163.co [College of Maths and Systematic Science, Shenyang Normal University, Shenyang 110034 (China)

2011-01-17

In this Letter, we consider the modified derivatives and integrals of fractional-order pseudo-differential operators. A sequence of Lax KP equations hierarchy and extended fractional KP (fKP) hierarchy are introduced, and the fKP hierarchy has Lax presentations with the extended Lax operators. In the case of the extension with the half-order pseudo-differential operators, a new integrable fKP hierarchy is obtained. A few particular examples of fractional order will be listed, together with their Lax pairs.

Chromium Fractions Changes Compared With Total-Cr As Determined by Neutron Activation Analysis Technique

International Nuclear Information System (INIS)

Abdel-Sabour, M.F.; Abdou, F.M.; Elwan, I.M.; Al-Salama, Y.J.

2003-01-01

Fifteen soil samples were chosen from different locations (five different locations at north greater Cairo, Egypt to represent different soils (alluvial and sandy) as well as different source of contaminated wastewater (sewage and industrial effluent). Using sequential extraction technique (extracting the soil with different solutions, which is designed to separate metal fractions), Cr was separated into six operationally defined fractions water soluble, exchangeable, carbonate bound, Fe-Mn oxides bound, organic bound and residual fractions. Result of soil total-Cr indicated the serious accumulation of Cr in soils subjected to prolonged irrigation with contaminated wastewater. As it could seen, total-Cr in the tested contaminated soils exceeds the permissible levels (75-100)ppm Cr by several order of magnitude particularly at the surface and subsurface layers. The highest accumulation of total Cr down to depth 60 cm was observed in case of soil E. Data showed that values of total Cr determined by NAA method were always higher than the relevant values determined either by AAS or those calculated after the sequential extraction method. T-test analysis showed the significant difference between NAA and either AAS or sequential extraction methods. Although T-test analysis showed that were significant differences between total content in soils as determined by destructive (AAS or SUM) and non-destructive (NAA) analytical techniques however, strong liner relation between NAA and other tested methods was obtained. Chromium distribution between different extractants shows that the greatest amounts are found in the residual and Occluded in Fe and Mn-Oxides fractions followed by carbonate or organic fractions. In most cases the proportion of all tested Cr-forms has increased in contaminated soil layers with higher enrichment in organically bound Cr, occluded in Fe and Mn oxides, carbonate exchangeable and soluble fractions. Results indicate that soil properties have a

On varitional iteration method for fractional calculus

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Wu Hai-Gen

2017-01-01

Full Text Available Modification of the Das’ variational iteration method for fractional differential equations is discussed, and its main shortcoming involved in the solution process is pointed out and overcome by using fractional power series. The suggested computational procedure is simple and reliable for fractional calculus.

A fast direct method for block triangular Toeplitz-like with tri-diagonal block systems from time-fractional partial differential equations

Science.gov (United States)

Ke, Rihuan; Ng, Michael K.; Sun, Hai-Wei

2015-12-01

In this paper, we study the block lower triangular Toeplitz-like with tri-diagonal blocks system which arises from the time-fractional partial differential equation. Existing fast numerical solver (e.g., fast approximate inversion method) cannot handle such linear system as the main diagonal blocks are different. The main contribution of this paper is to propose a fast direct method for solving this linear system, and to illustrate that the proposed method is much faster than the classical block forward substitution method for solving this linear system. Our idea is based on the divide-and-conquer strategy and together with the fast Fourier transforms for calculating Toeplitz matrix-vector multiplication. The complexity needs O (MNlog2 ⁡ M) arithmetic operations, where M is the number of blocks (the number of time steps) in the system and N is the size (number of spatial grid points) of each block. Numerical examples from the finite difference discretization of time-fractional partial differential equations are also given to demonstrate the efficiency of the proposed method.

An Operational Matrix Technique for Solving Variable Order Fractional Differential-Integral Equation Based on the Second Kind of Chebyshev Polynomials

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Jianping Liu

2016-01-01

Full Text Available An operational matrix technique is proposed to solve variable order fractional differential-integral equation based on the second kind of Chebyshev polynomials in this paper. The differential operational matrix and integral operational matrix are derived based on the second kind of Chebyshev polynomials. Using two types of operational matrixes, the original equation is transformed into the arithmetic product of several dependent matrixes, which can be viewed as an algebraic system after adopting the collocation points. Further, numerical solution of original equation is obtained by solving the algebraic system. Finally, several examples show that the numerical algorithm is computationally efficient.

Fractional Nottale's Scale Relativity and emergence of complexified gravity

International Nuclear Information System (INIS)

EL-Nabulsi, Ahmad Rami

2009-01-01

Fractional calculus of variations has recently gained significance in studying weak dissipative and nonconservative dynamical systems ranging from classical mechanics to quantum field theories. In this paper, fractional Nottale's Scale Relativity (NSR) for an arbitrary fractal dimension is introduced within the framework of fractional action-like variational approach recently introduced by the author. The formalism is based on fractional differential operators that generalize the differential operators of conventional NSR but that reduces to the standard formalism in the integer limit. Our main aim is to build the fractional setting for the NSR dynamical equations. Many interesting consequences arise, in particular the emergence of complexified gravity and complex time.

Mango (Mangifera indica L.) peel extract fractions from different cultivars differentially affect lipid accumulation in 3T3-L1 adipocyte cells.

Science.gov (United States)

Taing, Meng-Wong; Pierson, Jean-Thomas; Shaw, Paul N; Dietzgen, Ralf G; Roberts-Thomson, Sarah J; Gidley, Michael J; Monteith, Gregory R

2013-02-26

Plant phytochemicals are increasingly recognised as sources of bioactive molecules which may have potential benefit in many health conditions. In mangoes, peel extracts from different cultivars exhibit varying effects on adipogenesis in the 3T3-L1 adipocyte cell line. In this study, the effects of preparative HPLC fractions of methanol peel extracts from Irwin, Nam Doc Mai and Kensington Pride mangoes were evaluated. Fraction 1 contained the most hydrophilic components while subsequent fractions contained increasingly more hydrophobic components. High content imaging was used to assess mango peel fraction effects on lipid accumulation, nuclei count and nuclear area in differentiating 3T3-L1 cells. For all three mango cultivars, the more hydrophilic peel fractions 1-3 inhibited lipid accumulation with greater potency than the more hydrophobic peel fractions 4. For all three cultivars, the more lipophilic fraction 4 had concentrations that enhanced lipid accumulation greater than fractions 1-3 as assessed by lipid droplet integrated intensity. The potency of this fraction 4 varied significantly between cultivars. Using mass spectrometry, five long chain free fatty acids were detected in fraction 4; these were not present in any other peel extract fractions. Total levels varied between cultivars, with Irwin fraction 4 containing the highest levels of these free fatty acids. Lipophilic components appear to be responsible for the lipid accumulation promoting effects of some mango extracts and are the likely cause of the diverse effects of peel extracts from different mango cultivars on lipid accumulation.

Fractional Bateman—Feshbach Tikochinsky Oscillator

Science.gov (United States)

Dumitru, Baleanu; Jihad, H. Asad; Ivo, Petras

2014-02-01

In the last few years the numerical methods for solving the fractional differential equations started to be applied intensively to real world phenomena. Having these things in mind in this manuscript we focus on the fractional Lagrangian and Hamiltonian of the complex Bateman—Feshbach Tikochinsky oscillator. The numerical analysis of the corresponding fractional Euler-Lagrange equations is given within the Grünwald—Letnikov approach, which is power series expansion of the generating function.

Boundary value problems for multi-term fractional differential equations

Science.gov (United States)

Daftardar-Gejji, Varsha; Bhalekar, Sachin

2008-09-01

Multi-term fractional diffusion-wave equation along with the homogeneous/non-homogeneous boundary conditions has been solved using the method of separation of variables. It is observed that, unlike in the one term case, solution of multi-term fractional diffusion-wave equation is not necessarily non-negative, and hence does not represent anomalous diffusion of any kind.

Determination and partitioning of metals in sediments along the Suez Canal by sequential extraction

Science.gov (United States)

Abd El-Azim, H.; El-Moselhy, Kh. M.

2005-06-01

The application of sequential extraction technique was used to determine the chemical association of heavy metals in five different chemical phases (exchangeable F1, bound to carbonate F2, bound to Fe-Mn oxides F3, bound to organic matter F4 and residual F5) for sediment samples collected from the Suez Canal. From the obtained data, it can be seen that the surplus of metal contaminants introduced into the sediment from sources usually exists in relatively unstable chemical forms. A high proportion of the studied metals remained in the residual fraction. Most of remaining portion of metals was bound to ferromanganese oxides fraction. The low concentrations of metals in the exchangeable fraction indicated that the sediments of Suez Canal were relatively unpolluted.

New trends in nanotechnology and fractional calculus applications

CERN Document Server

Baleanu, Dumitru; Machado, JA Tenreiro

2010-01-01

In recent years, fractional calculus has played a major role in various fields such as mechanics, electricity, biology and economics. This book presents the state-of-the-art in the study of fractional systems and the application of fractional differentiation.

High Performance Computing for Solving Fractional Differential Equations with Applications

OpenAIRE

Zhang, Wei

2014-01-01

Fractional calculus is the generalization of integer-order calculus to rational order. This subject has at least three hundred years of history. However, it was traditionally regarded as a pure mathematical field and lacked real world applications for a very long time. In recent decades, fractional calculus has re-attracted the attention of scientists and engineers. For example, many researchers have found that fractional calculus is a useful tool for describing hereditary materials and p...

Analysis of fractional anisotropy facilitates differentiation of glioblastoma and brain metastases in a clinical setting

Energy Technology Data Exchange (ETDEWEB)

Bette, Stefanie, E-mail: stefanie.bette@tum.de [Department of Neuroradiology, Klinikum rechts der Isar, Technische Universität München, Munich (Germany); Huber, Thomas; Wiestler, Benedikt; Boeckh-Behrens, Tobias [Department of Neuroradiology, Klinikum rechts der Isar, Technische Universität München, Munich (Germany); Gempt, Jens; Ringel, Florian; Meyer, Bernhard [Department of Neurosurgery, Klinikum rechts der Isar, Technische Universität München, Munich (Germany); Zimmer, Claus; Kirschke, Jan S. [Department of Neuroradiology, Klinikum rechts der Isar, Technische Universität München, Munich (Germany)

2016-12-15

Purpose: Differentiating glioblastoma from brain metastases is important for therapy planning. Diffusion tensor imaging (DTI) was described as a promising tool, however with conflicting results. Aim: of this study was to analyze the clinical utility of DTI for the differentiation of brain metastases and glioblastoma. Methods: 294 patients (165 glioblastoma, 129 brain metastases) with preoperative DTI were included in this retrospective study. Fractional anisotropy (FA) was measured via regions of interest (ROIs) in the contrast-enhancing tumor, the necrosis and the FLAIR-hyperintense non-enhancing peritumoral region (NEPTR). Two neuroradiologists classified patient cases as glioblastoma or brain metastases without and with knowledge of FA values. Results: Glioblastoma showed significantly higher FA{sub contrast} (median glioblastoma = 0.33, metastases = 0.23; P < 0.001) whereas no significant difference was observed for FA{sub NEPTR} (0.21 vs. 0.22; P = 0.28) and for FA{sub necrosis} (0.17 vs. 0.18, P = 0.37). FA improved diagnostic accuracy of the neuroradiologists significantly from an AUC of 0.84/0.85 (Reader1/Reader2) to 0.89/0.92. Conclusions: Glioblastoma show significantly higher FA values in the contrast enhancing tumor part than brain metastases. Implementation of a ROI-based measurement of FA values and FA color maps in clinical routine helps to differentiate between glioblastoma and brain metastases.

Bifurcation and chaos of a new discrete fractional-order logistic map

Science.gov (United States)

Ji, YuanDong; Lai, Li; Zhong, SuChuan; Zhang, Lu

2018-04-01

The fractional-order discrete maps with chaotic behaviors based on the theory of ;fractional difference; are proposed in recent years. In this paper, instead of using fractional difference, a new fractionalized logistic map is proposed based on the numerical algorithm of fractional differentiation definition. The bifurcation diagrams of this map with various differential orders are given by numerical simulation. The simulation results show that the fractional-order logistic map derived in this manner holds rich dynamical behaviors because of its memory effect. In addition, new types of behaviors of bifurcation and chaos are found, which are different from those of the integer-order and the previous fractional-order logistic maps.

Fractional Delayer Utilizing Hermite Interpolation with Caratheodory Representation

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Qiang DU

2018-04-01

Full Text Available Fractional delay is indispensable for many sorts of circuits and signal processing applications. Fractional delay filter (FDF utilizing Hermite interpolation with an analog differentiator is a straightforward way to delay discrete signals. This method has a low time-domain error, but a complicated sampling module than the Shannon sampling scheme. A simplified scheme, which is based on Shannon sampling and utilizing Hermite interpolation with a digital differentiator, will lead a much higher time-domain error when the signal frequency approaches the Nyquist rate. In this letter, we propose a novel fractional delayer utilizing Hermite interpolation with Caratheodory representation. The samples of differential signal are obtained by Caratheodory representation from the samples of the original signal only. So, only one sampler is needed and the sampling module is simple. Simulation results for four types of signals demonstrate that the proposed method has significantly higher interpolation accuracy than Hermite interpolation with digital differentiator.

The respective effects of soil heavy metal fractions by sequential extraction procedure and soil properties on the accumulation of heavy metals in rice grains and brassicas.

Science.gov (United States)

Xiao, Ling; Guan, Dongsheng; Peart, M R; Chen, Yujuan; Li, Qiqi

2017-01-01

This study was carried out to examine heavy metal accumulation in rice grains and brassicas and to identify the different controls, such as soil properties and soil heavy metal fractions obtained by the Community Bureau of Reference (BCR) sequential extraction, in their accumulation. In Guangdong Province, South China, rice grain and brassica samples, along with their rhizospheric soil, were collected from fields on the basis of distance downstream from electroplating factories, whose wastewater was used for irrigation. The results showed that long-term irrigation using the electroplating effluent has not only enriched the rhizospheric soil with Cd, Cr, Cu, and Zn but has also increased their mobility and bioavailability. The average concentrations of Cd and Cr in rice grains and brassicas from closest to the electroplating factories were significantly higher than those from the control areas. Results from hybrid redundancy analysis (hRDA) and redundancy analysis (RDA) showed that the BCR fractions of soil heavy metals could explain 29.0 and 46.5 % of total eigenvalue for heavy metal concentrations in rice grains and brassicas, respectively, while soil properties could only explain 11.1 and 33.4 %, respectively. This indicated that heavy metal fractions exerted more control upon their concentrations in rice grains and brassicas than soil properties. In terms of metal interaction, an increase of residual Zn in paddy soil or a decrease of acid soluble Cd in the brassica soil could enhance the accumulation of Cd, Cu, Cr, and Pb in both rice grains and brassicas, respectively, while the reducible or oxidizable Cd in soil could enhance the plants' accumulation of Cr and Pb. The RDA showed an inhibition effect of sand content and CFO on the accumulation of heavy metals in rice grains and brassicas. Moreover, multiple stepwise linear regression could offer prediction for Cd, Cu, Cr, and Zn concentrations in the two crops by soil heavy metal fractions and soil properties.

An efficient algorithm for some highly nonlinear fractional PDEs in mathematical physics.

Directory of Open Access Journals (Sweden)

Jamshad Ahmad

Full Text Available In this paper, a fractional complex transform (FCT is used to convert the given fractional partial differential equations (FPDEs into corresponding partial differential equations (PDEs and subsequently Reduced Differential Transform Method (RDTM is applied on the transformed system of linear and nonlinear time-fractional PDEs. The results so obtained are re-stated by making use of inverse transformation which yields it in terms of original variables. It is observed that the proposed algorithm is highly efficient and appropriate for fractional PDEs and hence can be extended to other complex problems of diversified nonlinear nature.

Generalized Functions for the Fractional Calculus

Science.gov (United States)

Lorenzo, Carl F.; Hartley, Tom T.

1999-01-01

Previous papers have used two important functions for the solution of fractional order differential equations, the Mittag-Leffler functionE(sub q)[at(exp q)](1903a, 1903b, 1905), and the F-function F(sub q)[a,t] of Hartley & Lorenzo (1998). These functions provided direct solution and important understanding for the fundamental linear fractional order differential equation and for the related initial value problem (Hartley and Lorenzo, 1999). This paper examines related functions and their Laplace transforms. Presented for consideration are two generalized functions, the R-function and the G-function, useful in analysis and as a basis for computation in the fractional calculus. The R-function is unique in that it contains all of the derivatives and integrals of the F-function. The R-function also returns itself on qth order differ-integration. An example application of the R-function is provided. A further generalization of the R-function, called the G-function brings in the effects of repeated and partially repeated fractional poles.

Assessing metal contamination in recent creek sediments using fractionation technique along Mumbai coast, India

Digital Repository Service at National Institute of Oceanography (India)

Fernandes, L.L.; Nayak, G.N.

nitrogen) and sediment components (sand, silt, clay). A sequential extraction procedure was also applied to understand the partitioning of trace metals among the different fractions of the sediment. Together with this data, pollution indices were also...

Fermentation characteristics of polysaccharide fractions extracted from the cell walls of maize endosperm

NARCIS (Netherlands)

Laar, van H.; Tamminga, S.; Williams, B.A.; Verstegen, M.W.A.; Schols, H.A.

2002-01-01

Cell walls were extracted from maize endosperm and separated into different polysaccharide fractions by sequential extraction with solutions of saturated Ba(OH)2, demineralised water and 1 and 4 M KOH. Solubilised polysaccharides were collected after each extraction. Residues were collected

Fractional Bateman—Feshbach Tikochinsky Oscillator

International Nuclear Information System (INIS)

Baleanu, Dumitru; Asad, Jihad H.; Petras Ivo

2014-01-01

In the last few years the numerical methods for solving the fractional differential equations started to be applied intensively to real world phenomena. Having these things in mind in this manuscript we focus on the fractional Lagrangian and Hamiltonian of the complex Bateman—Feshbach Tikochinsky oscillator. The numerical analysis of the corresponding fractional Euler-Lagrange equations is given within the Grünwald—Letnikov approach, which is power series expansion of the generating function. (physics of elementary particles and fields)

Differential branching fraction and angular analysis of $\\Lambda^{0}_{b} \\rightarrow \\Lambda^0 \\mu^+\\mu^-$ decays

CERN Document Server

Aaij, Roel; Adinolfi, Marco; Affolder, Anthony; Ajaltouni, Ziad; Akar, Simon; Albrecht, Johannes; Alessio, Federico; Alexander, Michael; Ali, Suvayu; Alkhazov, Georgy; Alvarez Cartelle, Paula; Alves Jr, Antonio Augusto; Amato, Sandra; Amerio, Silvia; Amhis, Yasmine; An, Liupan; Anderlini, Lucio; Anderson, Jonathan; Andreotti, Mirco; Andrews, Jason; Appleby, Robert; Aquines Gutierrez, Osvaldo; Archilli, Flavio; Artamonov, Alexander; Artuso, Marina; Aslanides, Elie; Auriemma, Giulio; Baalouch, Marouen; Bachmann, Sebastian; Back, John; Badalov, Alexey; Baesso, Clarissa; Baldini, Wander; Barlow, Roger; Barschel, Colin; Barsuk, Sergey; Barter, William; Batozskaya, Varvara; Battista, Vincenzo; Bay, Aurelio; Beaucourt, Leo; Beddow, John; Bedeschi, Franco; Bediaga, Ignacio; Bel, Lennaert; Belyaev, Ivan; Ben-Haim, Eli; Bencivenni, Giovanni; Benson, Sean; Benton, Jack; Berezhnoy, Alexander; Bernet, Roland; Bertolin, Alessandro; Bettler, Marc-Olivier; van Beuzekom, Martinus; Bien, Alexander; Bifani, Simone; Bird, Thomas; Bizzeti, Andrea; Blake, Thomas; Blanc, Frédéric; Blouw, Johan; Blusk, Steven; Bocci, Valerio; Bondar, Alexander; Bondar, Nikolay; Bonivento, Walter; Borghi, Silvia; Borsato, Martino; Bowcock, Themistocles; Bowen, Espen Eie; Bozzi, Concezio; Braun, Svende; Brett, David; Britsch, Markward; Britton, Thomas; Brodzicka, Jolanta; Brook, Nicholas; Bursche, Albert; Buytaert, Jan; Cadeddu, Sandro; Calabrese, Roberto; Calvi, Marta; Calvo Gomez, Miriam; Campana, Pierluigi; Campora Perez, Daniel; Capriotti, Lorenzo; Carbone, Angelo; Carboni, Giovanni; Cardinale, Roberta; Cardini, Alessandro; Carniti, Paolo; Carson, Laurence; Carvalho Akiba, Kazuyoshi; Casanova Mohr, Raimon; Casse, Gianluigi; Cassina, Lorenzo; Castillo Garcia, Lucia; Cattaneo, Marco; Cauet, Christophe; Cavallero, Giovanni; Cenci, Riccardo; Charles, Matthew; Charpentier, Philippe; Chefdeville, Maximilien; Chen, Shanzhen; Cheung, Shu-Faye; Chiapolini, Nicola; Chrzaszcz, Marcin; Cid Vidal, Xabier; Ciezarek, Gregory; Clarke, Peter; Clemencic, Marco; Cliff, Harry; Closier, Joel; Coco, Victor; Cogan, Julien; Cogneras, Eric; Cogoni, Violetta; Cojocariu, Lucian; Collazuol, Gianmaria; Collins, Paula; Comerma-Montells, Albert; Contu, Andrea; Cook, Andrew; Coombes, Matthew; Coquereau, Samuel; Corti, Gloria; Corvo, Marco; Counts, Ian; Couturier, Benjamin; Cowan, Greig; Craik, Daniel Charles; Crocombe, Andrew; Cruz Torres, Melissa Maria; Cunliffe, Samuel; Currie, Robert; D'Ambrosio, Carmelo; Dalseno, Jeremy; David, Pieter; Davis, Adam; De Bruyn, Kristof; De Capua, Stefano; De Cian, Michel; De Miranda, Jussara; De Paula, Leandro; De Silva, Weeraddana; De Simone, Patrizia; Dean, Cameron Thomas; Decamp, Daniel; Deckenhoff, Mirko; Del Buono, Luigi; Déléage, Nicolas; Derkach, Denis; Deschamps, Olivier; Dettori, Francesco; Dey, Biplab; Di Canto, Angelo; Di Ruscio, Francesco; Dijkstra, Hans; Donleavy, Stephanie; Dordei, Francesca; Dorigo, Mirco; Dosil Suárez, Alvaro; Dossett, David; Dovbnya, Anatoliy; Dreimanis, Karlis; Dujany, Giulio; Dupertuis, Frederic; Durante, Paolo; Dzhelyadin, Rustem; Dziurda, Agnieszka; Dzyuba, Alexey; Easo, Sajan; Egede, Ulrik; Egorychev, Victor; Eidelman, Semen; Eisenhardt, Stephan; Eitschberger, Ulrich; Ekelhof, Robert; Eklund, Lars; El Rifai, Ibrahim; Elsasser, Christian; Ely, Scott; Esen, Sevda; Evans, Hannah Mary; Evans, Timothy; Falabella, Antonio; Färber, Christian; Farinelli, Chiara; Farley, Nathanael; Farry, Stephen; Fay, Robert; Ferguson, Dianne; Fernandez Albor, Victor; Ferrari, Fabio; Ferreira Rodrigues, Fernando; Ferro-Luzzi, Massimiliano; Filippov, Sergey; Fiore, Marco; Fiorini, Massimiliano; Firlej, Miroslaw; Fitzpatrick, Conor; Fiutowski, Tomasz; Fol, Philip; Fontana, Marianna; Fontanelli, Flavio; Forty, Roger; Francisco, Oscar; Frank, Markus; Frei, Christoph; Frosini, Maddalena; Fu, Jinlin; Furfaro, Emiliano; Gallas Torreira, Abraham; Galli, Domenico; Gallorini, Stefano; Gambetta, Silvia; Gandelman, Miriam; Gandini, Paolo; Gao, Yuanning; García Pardiñas, Julián; Garofoli, Justin; Garra Tico, Jordi; Garrido, Lluis; Gascon, David; Gaspar, Clara; Gastaldi, Ugo; Gauld, Rhorry; Gavardi, Laura; Gazzoni, Giulio; Geraci, Angelo; Gerick, David; Gersabeck, Evelina; Gersabeck, Marco; Gershon, Timothy; Ghez, Philippe; Gianelle, Alessio; Gianì, Sebastiana; Gibson, Valerie; Giubega, Lavinia-Helena; Gligorov, Vladimir; Göbel, Carla; Golubkov, Dmitry; Golutvin, Andrey; Gomes, Alvaro; Gotti, Claudio; Grabalosa Gándara, Marc; Graciani Diaz, Ricardo; Granado Cardoso, Luis Alberto; Graugés, Eugeni; Graverini, Elena; Graziani, Giacomo; Grecu, Alexandru; Greening, Edward; Gregson, Sam; Griffith, Peter; Grillo, Lucia; Grünberg, Oliver; Gui, Bin; Gushchin, Evgeny; Guz, Yury; Gys, Thierry; Hadjivasiliou, Christos; Haefeli, Guido; Haen, Christophe; Haines, Susan; Hall, Samuel; Hamilton, Brian; Hampson, Thomas; Han, Xiaoxue; Hansmann-Menzemer, Stephanie; Harnew, Neville; Harnew, Samuel; Harrison, Jonathan; He, Jibo; Head, Timothy; Heijne, Veerle; Hennessy, Karol; Henrard, Pierre; Henry, Louis; Hernando Morata, Jose Angel; van Herwijnen, Eric; Heß, Miriam; Hicheur, Adlène; Hill, Donal; Hoballah, Mostafa; Hombach, Christoph; Hulsbergen, Wouter; Humair, Thibaud; Hussain, Nazim; Hutchcroft, David; Hynds, Daniel; Idzik, Marek; Ilten, Philip; Jacobsson, Richard; Jaeger, Andreas; Jalocha, Pawel; Jans, Eddy; Jawahery, Abolhassan; Jing, Fanfan; John, Malcolm; Johnson, Daniel; Jones, Christopher; Joram, Christian; Jost, Beat; Jurik, Nathan; Kandybei, Sergii; Kanso, Walaa; Karacson, Matthias; Karbach, Moritz; Karodia, Sarah; Kelsey, Matthew; Kenyon, Ian; Kenzie, Matthew; Ketel, Tjeerd; Khanji, Basem; Khurewathanakul, Chitsanu; Klaver, Suzanne; Klimaszewski, Konrad; Kochebina, Olga; Kolpin, Michael; Komarov, Ilya; Koopman, Rose; Koppenburg, Patrick; Korolev, Mikhail; Kravchuk, Leonid; Kreplin, Katharina; Kreps, Michal; Krocker, Georg; Krokovny, Pavel; Kruse, Florian; Kucewicz, Wojciech; Kucharczyk, Marcin; Kudryavtsev, Vasily; Kurek, Krzysztof; Kvaratskheliya, Tengiz; La Thi, Viet Nga; Lacarrere, Daniel; Lafferty, George; Lai, Adriano; Lambert, Dean; Lambert, Robert W; Lanfranchi, Gaia; Langenbruch, Christoph; Langhans, Benedikt; Latham, Thomas; Lazzeroni, Cristina; Le Gac, Renaud; van Leerdam, Jeroen; Lees, Jean-Pierre; Lefèvre, Regis; Leflat, Alexander; Lefrançois, Jacques; Leroy, Olivier; Lesiak, Tadeusz; Leverington, Blake; Li, Yiming; Likhomanenko, Tatiana; Liles, Myfanwy; Lindner, Rolf; Linn, Christian; Lionetto, Federica; Liu, Bo; Lohn, Stefan; Longstaff, Iain; Lopes, Jose; Lowdon, Peter; Lucchesi, Donatella; Luo, Haofei; Lupato, Anna; Luppi, Eleonora; Lupton, Oliver; Machefert, Frederic; Maciuc, Florin; Maev, Oleg; Malde, Sneha; Malinin, Alexander; Manca, Giulia; Mancinelli, Giampiero; Manning, Peter Michael; Mapelli, Alessandro; Maratas, Jan; Marchand, Jean François; Marconi, Umberto; Marin Benito, Carla; Marino, Pietro; Märki, Raphael; Marks, Jörg; Martellotti, Giuseppe; Martinelli, Maurizio; Martinez Santos, Diego; Martinez Vidal, Fernando; Martins Tostes, Danielle; Massafferri, André; Matev, Rosen; Mathad, Abhijit; Mathe, Zoltan; Matteuzzi, Clara; Mauri, Andrea; Maurin, Brice; Mazurov, Alexander; McCann, Michael; McCarthy, James; McNab, Andrew; McNulty, Ronan; Meadows, Brian; Meier, Frank; Meissner, Marco; Merk, Marcel; Milanes, Diego Alejandro; Minard, Marie-Noelle; Mitzel, Dominik Stefan; Molina Rodriguez, Josue; Monteil, Stephane; Morandin, Mauro; Morawski, Piotr; Mordà, Alessandro; Morello, Michael Joseph; Moron, Jakub; Morris, Adam Benjamin; Mountain, Raymond; Muheim, Franz; Müller, Katharina; Mussini, Manuel; Muster, Bastien; Naik, Paras; Nakada, Tatsuya; Nandakumar, Raja; Nasteva, Irina; Needham, Matthew; Neri, Nicola; Neubert, Sebastian; Neufeld, Niko; Neuner, Max; Nguyen, Anh Duc; Nguyen, Thi-Dung; Nguyen-Mau, Chung; Niess, Valentin; Niet, Ramon; Nikitin, Nikolay; Nikodem, Thomas; Novoselov, Alexey; O'Hanlon, Daniel Patrick; Oblakowska-Mucha, Agnieszka; Obraztsov, Vladimir; Ogilvy, Stephen; Okhrimenko, Oleksandr; Oldeman, Rudolf; Onderwater, Gerco; Osorio Rodrigues, Bruno; Otalora Goicochea, Juan Martin; Otto, Adam; Owen, Patrick; Oyanguren, Maria Aranzazu; Palano, Antimo; Palombo, Fernando; Palutan, Matteo; Panman, Jacob; Papanestis, Antonios; Pappagallo, Marco; Pappalardo, Luciano; Parkes, Christopher; Passaleva, Giovanni; Patel, Girish; Patel, Mitesh; Patrignani, Claudia; Pearce, Alex; Pellegrino, Antonio; Penso, Gianni; Pepe Altarelli, Monica; Perazzini, Stefano; Perret, Pascal; Pescatore, Luca; Petridis, Konstantin; Petrolini, Alessandro; Picatoste Olloqui, Eduardo; Pietrzyk, Boleslaw; Pilař, Tomas; Pinci, Davide; Pistone, Alessandro; Playfer, Stephen; Plo Casasus, Maximo; Poikela, Tuomas; Polci, Francesco; Poluektov, Anton; Polyakov, Ivan; Polycarpo, Erica; Popov, Alexander; Popov, Dmitry; Popovici, Bogdan; Potterat, Cédric; Price, Eugenia; Price, Joseph David; Prisciandaro, Jessica; Pritchard, Adrian; Prouve, Claire; Pugatch, Valery; Puig Navarro, Albert; Punzi, Giovanni; Qian, Wenbin; Quagliani, Renato; Rachwal, Bartolomiej; Rademacker, Jonas; Rakotomiaramanana, Barinjaka; Rama, Matteo; Rangel, Murilo; Raniuk, Iurii; Rauschmayr, Nathalie; Raven, Gerhard; Redi, Federico; Reichert, Stefanie; Reid, Matthew; dos Reis, Alberto; Ricciardi, Stefania; Richards, Sophie; Rihl, Mariana; Rinnert, Kurt; Rives Molina, Vincente; Robbe, Patrick; Rodrigues, Ana Barbara; Rodrigues, Eduardo; Rodriguez Lopez, Jairo Alexis; Rodriguez Perez, Pablo; Roiser, Stefan; Romanovsky, Vladimir; Romero Vidal, Antonio; Rotondo, Marcello; Rouvinet, Julien; Ruf, Thomas; Ruiz, Hugo; Ruiz Valls, Pablo; Saborido Silva, Juan Jose; Sagidova, Naylya; Sail, Paul; Saitta, Biagio; Salustino Guimaraes, Valdir; Sanchez Mayordomo, Carlos; Sanmartin Sedes, Brais; Santacesaria, Roberta; Santamarina Rios, Cibran; Santovetti, Emanuele; Sarti, Alessio; Satriano, Celestina; Satta, Alessia; Saunders, Daniel Martin; Savrina, Darya; Schiller, Manuel; Schindler, Heinrich; Schlupp, Maximilian; Schmelling, Michael; Schmidt, Burkhard; Schneider, Olivier; Schopper, Andreas; Schune, Marie Helene; Schwemmer, Rainer; Sciascia, Barbara; Sciubba, Adalberto; Semennikov, Alexander; Sepp, Indrek; Serra, Nicola; Serrano, Justine; Sestini, Lorenzo; Seyfert, Paul; Shapkin, Mikhail; Shapoval, Illya; Shcheglov, Yury; Shears, Tara; Shekhtman, Lev; Shevchenko, Vladimir; Shires, Alexander; Silva Coutinho, Rafael; Simi, Gabriele; Sirendi, Marek; Skidmore, Nicola; Skillicorn, Ian; Skwarnicki, Tomasz; Smith, Anthony; Smith, Edmund; Smith, Eluned; Smith, Jackson; Smith, Mark; Snoek, Hella; Sokoloff, Michael; Soler, Paul; Soomro, Fatima; Souza, Daniel; Souza De Paula, Bruno; Spaan, Bernhard; Spradlin, Patrick; Sridharan, Srikanth; Stagni, Federico; Stahl, Marian; Stahl, Sascha; Steinkamp, Olaf; Stenyakin, Oleg; Sterpka, Christopher Francis; Stevenson, Scott; Stoica, Sabin; Stone, Sheldon; Storaci, Barbara; Stracka, Simone; Straticiuc, Mihai; Straumann, Ulrich; Stroili, Roberto; Sun, Liang; Sutcliffe, William; Swientek, Krzysztof; Swientek, Stefan; Syropoulos, Vasileios; Szczekowski, Marek; Szczypka, Paul; Szumlak, Tomasz; T'Jampens, Stephane; Teklishyn, Maksym; Tellarini, Giulia; Teubert, Frederic; Thomas, Christopher; Thomas, Eric; van Tilburg, Jeroen; Tisserand, Vincent; Tobin, Mark; Todd, Jacob; Tolk, Siim; Tomassetti, Luca; Tonelli, Diego; Topp-Joergensen, Stig; Torr, Nicholas; Tournefier, Edwige; Tourneur, Stephane; Trabelsi, Karim; Tran, Minh Tâm; Tresch, Marco; Trisovic, Ana; Tsaregorodtsev, Andrei; Tsopelas, Panagiotis; Tuning, Niels; Ukleja, Artur; Ustyuzhanin, Andrey; Uwer, Ulrich; Vacca, Claudia; Vagnoni, Vincenzo; Valenti, Giovanni; Vallier, Alexis; Vazquez Gomez, Ricardo; Vazquez Regueiro, Pablo; Vázquez Sierra, Carlos; Vecchi, Stefania; Velthuis, Jaap; Veltri, Michele; Veneziano, Giovanni; Vesterinen, Mika; Viana Barbosa, Joao Vitor; Viaud, Benoit; Vieira, Daniel; Vieites Diaz, Maria; Vilasis-Cardona, Xavier; Vollhardt, Achim; Volyanskyy, Dmytro; Voong, David; Vorobyev, Alexey; Vorobyev, Vitaly; Voß, Christian; de Vries, Jacco; Waldi, Roland; Wallace, Charlotte; Wallace, Ronan; Walsh, John; Wandernoth, Sebastian; Wang, Jianchun; Ward, David; Watson, Nigel; Websdale, David; Weiden, Andreas; Whitehead, Mark; Wiedner, Dirk; Wilkinson, Guy; Wilkinson, Michael; Williams, Mark Richard James; Williams, Matthew; Williams, Mike; Wilson, Fergus; Wimberley, Jack; Wishahi, Julian; Wislicki, Wojciech; Witek, Mariusz; Wormser, Guy; Wotton, Stephen; Wright, Simon; Wyllie, Kenneth; Xie, Yuehong; Xu, Zhirui; Yang, Zhenwei; Yuan, Xuhao; Yushchenko, Oleg; Zangoli, Maria; Zavertyaev, Mikhail; Zhang, Liming; Zhang, Yanxi; Zhelezov, Alexey; Zhokhov, Anatoly; Zhong, Liang

2015-01-01

The differential branching fraction of the rare decay $\\Lambda^{0}_{b} \\rightarrow \\Lambda^0 \\mu^+\\mu^-$ is measured as a function of $q^{2}$, the square of the dimuon invariant mass. The analysis is performed using proton-proton collision data, corresponding to an integrated luminosity of $3.0 \\mbox{ fb}^{-1}$, collected by the LHCb experiment. Evidence of signal is observed in the $q^2$ region below the square of the $J/\\psi$ mass. Integrating over $15 < q^{2} < 20 \\mbox{ GeV}^2/c^4$ the branching fraction is measured as $d\\mathcal{B}(\\Lambda^{0}_{b} \\rightarrow \\Lambda^0 \\mu^+\\mu^-)/dq^2 = (1.18 ^{+ 0.09} _{-0.08} \\pm 0.03 \\pm 0.27) \\times 10^{-7} ( \\mbox{GeV}^{2}/c^{4})^{-1}$, where the uncertainties are statistical, systematic and due to the normalisation mode, $\\Lambda^{0}_{b} \\rightarrow J/\\psi \\Lambda^0$, respectively. In the $q^2$ intervals where the signal is observed, angular distributions are studied and the forward-backward asymmetries in the dimuon ($A^{l}_{\\rm FB}$) and hadron ($A^{h}_{\\r...

An Efficient Implicit FEM Scheme for Fractional-in-Space Reaction-Diffusion Equations

KAUST Repository

Burrage, Kevin; Hale, Nicholas; Kay, David

2012-01-01

Fractional differential equations are becoming increasingly used as a modelling tool for processes associated with anomalous diffusion or spatial heterogeneity. However, the presence of a fractional differential operator causes memory (time

Numerical Analysis of Fractional Order Epidemic Model of Childhood Diseases

Directory of Open Access Journals (Sweden)

Fazal Haq

2017-01-01

Full Text Available The fractional order Susceptible-Infected-Recovered (SIR epidemic model of childhood disease is considered. Laplace–Adomian Decomposition Method is used to compute an approximate solution of the system of nonlinear fractional differential equations. We obtain the solutions of fractional differential equations in the form of infinite series. The series solution of the proposed model converges rapidly to its exact value. The obtained results are compared with the classical case.

Boundary Controllability of Nonlinear Fractional Integrodifferential Systems

Directory of Open Access Journals (Sweden)

Ahmed HamdyM

2010-01-01

Full Text Available Sufficient conditions for boundary controllability of nonlinear fractional integrodifferential systems in Banach space are established. The results are obtained by using fixed point theorems. We also give an application for integropartial differential equations of fractional order.

Sequentially-crosslinked biomimetic bioactive glass/gelatin methacryloyl composites hydrogels for bone regeneration.

Science.gov (United States)

Zheng, Jiafu; Zhao, Fujian; Zhang, Wen; Mo, Yunfei; Zeng, Lei; Li, Xian; Chen, Xiaofeng

2018-08-01

In recent years, gelatin-based composites hydrogels have been intensively investigated because of their inherent bioactivity, biocompatibility and biodegradability. Herein, we fabricated photocrosslinkable biomimetic composites hydrogels from bioactive glass (BG) and gelatin methacryloyl (GelMA) by a sequential physical and chemical crosslinking (gelation + UV) approach. The results showed that the compressive modulus of composites hydrogels increased significantly through the sequential crosslinking approach. The addition of BG resulted in a significant increase in physiological stability and apatite-forming ability. In vitro data indicated that BG/GelMA composites hydrogels promoted cell attachment, proliferation and differentiation. Overall, the BG/GelMA composites hydrogels combined the advantages of good biocompatibility and bioactivity, and had potential applications in bone regeneration. Copyright © 2018. Published by Elsevier B.V.

Shared and differentiated motor skill impairments in children with dyslexia and/or attention deficit disorder: From simple to complex sequential coordination.

Directory of Open Access Journals (Sweden)

Marie-Ève Marchand-Krynski

Full Text Available Dyslexia and Attention deficit disorder (AD are prevalent neurodevelopmental conditions in children and adolescents. They have high comorbidity rates and have both been associated with motor difficulties. Little is known, however, about what is shared or differentiated in dyslexia and AD in terms of motor abilities. Even when motor skill problems are identified, few studies have used the same measurement tools, resulting in inconstant findings. The present study assessed increasingly complex gross motor skills in children and adolescents with dyslexia, AD, and with both Dyslexia and AD. Our results suggest normal performance on simple motor-speed tests, whereas all three groups share a common impairment on unimanual and bimanual sequential motor tasks. Children in these groups generally improve with practice to the same level as normal subjects, though they make more errors. In addition, children with AD are the most impaired on complex bimanual out-of-phase movements and with manual dexterity. These latter findings are examined in light of the Multiple Deficit Model.

Organic phosphorus fractionation in wetland soil profiles by chemical extraction and phosphorus-31 nuclear magnetic resonance spectroscopy

International Nuclear Information System (INIS)

Li, Min; Zhang, Jing; Wang, Guangqian; Yang, Haijun; Whelan, Michael J.; White, Sue M.

2013-01-01

Highlights: ► Chemical sequential extraction and 31 P NMR spectroscopy were used for organic P analysis. ► Organic P includes orthophosphate, monoester and diester phosphate and pyrophosphate. ► Highly resistant organic P and monoester phosphate were the dominant organic P. ► HCl pretreatment can remove most inorganic P and increase organic P recovery rate. ► A comprehensive organic P chemical sequential fractionation approach was proposed. - Abstract: Organic P (OP) plays an important role in soil P cycling and is a potential P source for wetland plants. In this study, a modified chemical sequential fractionation method and 31 P nuclear magnetic resonance spectroscopy ( 31 P NMR) of NaOH–EDTA extracts were used to examine the distribution of organic P fractions and compounds in soil profiles of the Beijing Yeyahu Wetland, China. The influence of acid treatment prior to NaOH–EDTA extraction on 31 P NMR spectra was also investigated. Results show that highly resistant OP was the major class of organic P. The rank order of organic P fractions was highly resistant OP (on average accounting for 68.5% of total OP) > moderately resistant OP (15.8%m of total OP) > moderately labile OP (11.4% of total OP) > labile OP (4.3% of total OP). Most of the organic P fractions decreased with soil depth due to the accumulation of plant residues in surface soils and the deposition and diagenesis of soils. Moderately (r = 0.586, p < 0.01) and highly (r = 0.741, p < 0.01) resistant OP fractions were positively correlated with soil organic matter. Phosphorus compounds including orthophosphate (23–74.6% of total P in spectra), monoester phosphate (18.6–76%), diester phosphate (nil-7.8%) and pyrophosphate (nil-6.7%) were characterized using 31 P NMR. Monoester-P was the dominant soil organic P compound identified. The proportion of monoester-P increased significantly in NaOH–EDTA extracts with HCl pretreatment and it was confirmed by chemical analysis. Therefore, it

Adaptive Replanning to Account for Lumpectomy Cavity Change in Sequential Boost After Whole-Breast Irradiation

Energy Technology Data Exchange (ETDEWEB)

Chen, Xiaojian [Department of Radiation Oncology, Medical College of Wisconsin, Milwaukee, Wisconsin (United States); Qiao, Qiao [Department of Radiation Oncology, Medical College of Wisconsin, Milwaukee, Wisconsin (United States); Department of Radiotherapy, First Hospital of China Medical University, Shenyang (China); DeVries, Anthony [Department of Radiation Oncology, Medical College of Wisconsin, Milwaukee, Wisconsin (United States); Li, Wenhui [Department of Radiation Oncology, Medical College of Wisconsin, Milwaukee, Wisconsin (United States); Department of Radiotherapy, Yunnan Tumor Hospital, Kunming (China); Currey, Adam; Kelly, Tracy; Bergom, Carmen; Wilson, J. Frank [Department of Radiation Oncology, Medical College of Wisconsin, Milwaukee, Wisconsin (United States); Li, X. Allen, E-mail: ali@mcw.edu [Department of Radiation Oncology, Medical College of Wisconsin, Milwaukee, Wisconsin (United States)

2014-12-01

Purpose: To evaluate the efficiency of standard image-guided radiation therapy (IGRT) to account for lumpectomy cavity (LC) variation during whole-breast irradiation (WBI) and propose an adaptive strategy to improve dosimetry if IGRT fails to address the interfraction LC variations. Methods and Materials: Daily diagnostic-quality CT data acquired during IGRT in the boost stage using an in-room CT for 19 breast cancer patients treated with sequential boost after WBI in the prone position were retrospectively analyzed. Contours of the LC, treated breast, ipsilateral lung, and heart were generated by populating contours from planning CTs to boost fraction CTs using an auto-segmentation tool with manual editing. Three plans were generated on each fraction CT: (1) a repositioning plan by applying the original boost plan with the shift determined by IGRT; (2) an adaptive plan by modifying the original plan according to a fraction CT; and (3) a reoptimization plan by a full-scale optimization. Results: Significant variations were observed in LC. The change in LC volume at the first boost fraction ranged from a 70% decrease to a 50% increase of that on the planning CT. The adaptive and reoptimization plans were comparable. Compared with the repositioning plans, the adaptive plans led to an improvement in target coverage for an increased LC case (1 of 19, 7.5% increase in planning target volume evaluation volume V{sub 95%}), and breast tissue sparing for an LC decrease larger than 35% (3 of 19, 7.5% decrease in breast evaluation volume V{sub 50%}; P=.008). Conclusion: Significant changes in LC shape and volume at the time of boost that deviate from the original plan for WBI with sequential boost can be addressed by adaptive replanning at the first boost fraction.

Sequential growth factor application in bone marrow stromal cell ligament engineering.

Science.gov (United States)

Moreau, Jodie E; Chen, Jingsong; Horan, Rebecca L; Kaplan, David L; Altman, Gregory H

2005-01-01

In vitro bone marrow stromal cell (BMSC) growth may be enhanced through culture medium supplementation, mimicking the biochemical environment in which cells optimally proliferate and differentiate. We hypothesize that the sequential administration of growth factors to first proliferate and then differentiate BMSCs cultured on silk fiber matrices will support the enhanced development of ligament tissue in vitro. Confluent second passage (P2) BMSCs obtained from purified bone marrow aspirates were seeded on RGD-modified silk matrices. Seeded matrices were divided into three groups for 5 days of static culture, with medium supplement of basic fibroblast growth factor (B) (1 ng/mL), epidermal growth factor (E; 1 ng/mL), or growth factor-free control (C). After day 5, medium supplementation was changed to transforming growth factor-beta1 (T; 5 ng/mL) or C for an additional 9 days of culture. Real-time RT-PCR, SEM, MTT, histology, and ELISA for collagen type I of all sample groups were performed. Results indicated that BT supported the greatest cell ingrowth after 14 days of culture in addition to the greatest cumulative collagen type I expression measured by ELISA. Sequential growth factor application promoted significant increases in collagen type I transcript expression from day 5 of culture to day 14, for five of six groups tested. All T-supplemented samples surpassed their respective control samples in both cell ingrowth and collagen deposition. All samples supported spindle-shaped, fibroblast cell morphology, aligning with the direction of silk fibers. These findings indicate significant in vitro ligament development after only 14 days of culture when using a sequential growth factor approach.

Modelling sequentially scored item responses

NARCIS (Netherlands)

Akkermans, W.

2000-01-01

The sequential model can be used to describe the variable resulting from a sequential scoring process. In this paper two more item response models are investigated with respect to their suitability for sequential scoring: the partial credit model and the graded response model. The investigation is

Decision-making in research tasks with sequential testing.

Directory of Open Access Journals (Sweden)

Thomas Pfeiffer

Full Text Available BACKGROUND: In a recent controversial essay, published by JPA Ioannidis in PLoS Medicine, it has been argued that in some research fields, most of the published findings are false. Based on theoretical reasoning it can be shown that small effect sizes, error-prone tests, low priors of the tested hypotheses and biases in the evaluation and publication of research findings increase the fraction of false positives. These findings raise concerns about the reliability of research. However, they are based on a very simple scenario of scientific research, where single tests are used to evaluate independent hypotheses. METHODOLOGY/PRINCIPAL FINDINGS: In this study, we present computer simulations and experimental approaches for analyzing more realistic scenarios. In these scenarios, research tasks are solved sequentially, i.e. subsequent tests can be chosen depending on previous results. We investigate simple sequential testing and scenarios where only a selected subset of results can be published and used for future rounds of test choice. Results from computer simulations indicate that for the tasks analyzed in this study, the fraction of false among the positive findings declines over several rounds of testing if the most informative tests are performed. Our experiments show that human subjects frequently perform the most informative tests, leading to a decline of false positives as expected from the simulations. CONCLUSIONS/SIGNIFICANCE: For the research tasks studied here, findings tend to become more reliable over time. We also find that the performance in those experimental settings where not all performed tests could be published turned out to be surprisingly inefficient. Our results may help optimize existing procedures used in the practice of scientific research and provide guidance for the development of novel forms of scholarly communication.

R-Function Relationships for Application in the Fractional Calculus

Science.gov (United States)

Lorenzo, Carl F.; Hartley, Tom T.

2000-01-01

The F-function, and its generalization the R-function, are of fundamental importance in the fractional calculus. It has been shown that the solution of the fundamental linear fractional differential equation may be expressed in terms of these functions. These functions serve as generalizations of the exponential function in the solution of fractional differential equations. Because of this central role in the fractional calculus, this paper explores various intrarelationships of the R-function, which will be useful in further analysis. Relationships of the R-function to the common exponential function, e(t), and its fractional derivatives are shown. From the relationships developed, some important approximations are observed. Further, the inverse relationships of the exponential function, el, in terms of the R-function are developed. Also, some approximations for the R-function are developed.

Importance of fractional exhaled nitric oxide in the differentiation of asthma–COPD overlap syndrome, asthma, and COPD

Directory of Open Access Journals (Sweden)

Chen FJ

2016-09-01

Full Text Available Feng-jia Chen,* Xin-yan Huang,* Yang-li Liu, Geng-peng Lin, Can-mao Xie Department of Respiratory Disease, The First Affiliated Hospital, Sun Yat-sen University, Guangzhou, People’s Republic of China *These authors contributed equally to this work Background: Fractional exhaled nitric oxide (FeNO is an easy, sensitive, reproducible, and noninvasive marker of eosinophilic airway inflammation. Accordingly, FeNO is extensively used to diagnose and manage asthma. Patients with COPD who share some of the features of asthma have a condition called asthma–COPD overlap syndrome (ACOS. The feasibility of using FeNO to differentiate ACOS patients from asthma and COPD patients remains unclear. Methods: From February 2013 to May 2016, patients suspected with asthma and COPD through physician’s opinion were subjected to FeNO measurement, pulmonary function test (PFT, and bronchial hyperresponsiveness or bronchodilator test. Patients were divided into asthma alone group, COPD alone group, and ACOS group according to a clinical history, PFT values, and bronchial hyperresponsiveness or bronchodilator test. Receiver operating characteristic (ROC curves were obtained to elucidate the clinical functions of FeNO in diagnosing ACOS. The optimal operating point was also determined. Results: A total of 689 patients were enrolled in this study: 500 had asthma, 132 had COPD, and 57 had ACOS. The FeNO value in patients with ACOS was 27 (21.5 parts per billion (ppb; median [interquartile range], which was significantly higher than that in the COPD group (18 [11] ppb. The area under the ROC curve was estimated to be 0.783 for FeNO. Results also revealed an optimal cutoff value of >22.5 ppb FeNO for differentiating ACOS from COPD patients (sensitivity 70%, specificity 75%.Conclusion: FeNO measurement is an easy, noninvasive, and sensitive method for differentiating ACOS from COPD. This technique is a new perspective for the management of COPD patients. Keywords

Fractional power-law spatial dispersion in electrodynamics

International Nuclear Information System (INIS)

Tarasov, Vasily E.; Trujillo, Juan J.

2013-01-01

Electric fields in non-local media with power-law spatial dispersion are discussed. Equations involving a fractional Laplacian in the Riesz form that describe the electric fields in such non-local media are studied. The generalizations of Coulomb’s law and Debye’s screening for power-law non-local media are characterized. We consider simple models with anomalous behavior of plasma-like media with power-law spatial dispersions. The suggested fractional differential models for these plasma-like media are discussed to describe non-local properties of power-law type. -- Highlights: •Plasma-like non-local media with power-law spatial dispersion. •Fractional differential equations for electric fields in the media. •The generalizations of Coulomb’s law and Debye’s screening for the media

Multi-agent sequential hypothesis testing

KAUST Repository

Kim, Kwang-Ki K.

2014-12-15

This paper considers multi-agent sequential hypothesis testing and presents a framework for strategic learning in sequential games with explicit consideration of both temporal and spatial coordination. The associated Bayes risk functions explicitly incorporate costs of taking private/public measurements, costs of time-difference and disagreement in actions of agents, and costs of false declaration/choices in the sequential hypothesis testing. The corresponding sequential decision processes have well-defined value functions with respect to (a) the belief states for the case of conditional independent private noisy measurements that are also assumed to be independent identically distributed over time, and (b) the information states for the case of correlated private noisy measurements. A sequential investment game of strategic coordination and delay is also discussed as an application of the proposed strategic learning rules.

Testing sequential extraction methods for the analysis of multiple stable isotope systems from a bone sample

Science.gov (United States)

Sahlstedt, Elina; Arppe, Laura

2017-04-01

Stable isotope composition of bones, analysed either from the mineral phase (hydroxyapatite) or from the organic phase (mainly collagen) carry important climatological and ecological information and are therefore widely used in paleontological and archaeological research. For the analysis of the stable isotope compositions, both of the phases, hydroxyapatite and collagen, have their more or less well established separation and analytical techniques. Recent development in IRMS and wet chemical extraction methods have facilitated the analysis of very small bone fractions (500 μg or less starting material) for PO43-O isotope composition. However, the uniqueness and (pre-) historical value of each archaeological and paleontological finding lead to preciously little material available for stable isotope analyses, encouraging further development of microanalytical methods for the use of stable isotope analyses. Here we present the first results in developing extraction methods for combining collagen C- and N-isotope analyses to PO43-O-isotope analyses from a single bone sample fraction. We tested sequential extraction starting with dilute acid demineralization and collection of both collagen and PO43-fractions, followed by further purification step by H2O2 (PO43-fraction). First results show that bone sample separates as small as 2 mg may be analysed for their δ15N, δ13C and δ18OPO4 values. The method may be incorporated in detailed investigation of sequentially developing skeletal material such as teeth, potentially allowing for the investigation of interannual variability in climatological/environmental signals or investigation of the early life history of an individual.

Fractional Nottale's Scale Relativity and emergence of complexified gravity

Energy Technology Data Exchange (ETDEWEB)

EL-Nabulsi, Ahmad Rami [Department of Nuclear and Energy Engineering, Cheju National University, Ara-dong 1, Jeju 690-756 (Korea, Republic of)], E-mail: nabulsiahmadrami@yahoo.fr

2009-12-15

Fractional calculus of variations has recently gained significance in studying weak dissipative and nonconservative dynamical systems ranging from classical mechanics to quantum field theories. In this paper, fractional Nottale's Scale Relativity (NSR) for an arbitrary fractal dimension is introduced within the framework of fractional action-like variational approach recently introduced by the author. The formalism is based on fractional differential operators that generalize the differential operators of conventional NSR but that reduces to the standard formalism in the integer limit. Our main aim is to build the fractional setting for the NSR dynamical equations. Many interesting consequences arise, in particular the emergence of complexified gravity and complex time.

Electronically Tunable Fully Integrated Fractional-Order Resonator

KAUST Repository

Tsirimokou, Georgia

2017-03-20

A fully integrated implementation of a parallel fractional-order resonator which employs together a fractional order capacitor and a fractional-order inductor is proposed in this paper. The design utilizes current-controlled Operational Transconductance Amplifiers as building blocks, designed and fabricated in AMS 0:35m CMOS process, and based on a second-order approximation of a fractional-order differentiator/ integrator magnitude optimized in the range 10Hz–700Hz. An attractive benefit of the proposed scheme is its electronic tuning capability.

Electronically Tunable Fully Integrated Fractional-Order Resonator

KAUST Repository

Tsirimokou, Georgia; Psychalinos, Costas; Elwakil, Ahmed S.; Salama, Khaled N.

2017-01-01

A fully integrated implementation of a parallel fractional-order resonator which employs together a fractional order capacitor and a fractional-order inductor is proposed in this paper. The design utilizes current-controlled Operational Transconductance Amplifiers as building blocks, designed and fabricated in AMS 0:35m CMOS process, and based on a second-order approximation of a fractional-order differentiator/ integrator magnitude optimized in the range 10Hz–700Hz. An attractive benefit of the proposed scheme is its electronic tuning capability.

Sequential charged particle reaction

International Nuclear Information System (INIS)

Hori, Jun-ichi; Ochiai, Kentaro; Sato, Satoshi; Yamauchi, Michinori; Nishitani, Takeo

2004-01-01

The effective cross sections for producing the sequential reaction products in F82H, pure vanadium and LiF with respect to the 14.9-MeV neutron were obtained and compared with the estimation ones. Since the sequential reactions depend on the secondary charged particles behavior, the effective cross sections are corresponding to the target nuclei and the material composition. The effective cross sections were also estimated by using the EAF-libraries and compared with the experimental ones. There were large discrepancies between estimated and experimental values. Additionally, we showed the contribution of the sequential reaction on the induced activity and dose rate in the boundary region with water. From the present study, it has been clarified that the sequential reactions are of great importance to evaluate the dose rates around the surface of cooling pipe and the activated corrosion products. (author)

Ultracentrifugation for ultrafine nanodiamond fractionation

Science.gov (United States)

Koniakhin, S. V.; Besedina, N. A.; Kirilenko, D. A.; Shvidchenko, A. V.; Eidelman, E. D.

2018-01-01

In this paper we propose a method for ultrafine fractionation of nanodiamonds using the differential centrifugation in the fields up to 215000g. The developed protocols yield 4-6 nm fraction giving main contribution to the light scattering intensity. The desired 4-6 nm fraction can be obtained from various types of initial nanodiamonds: three types of detonation nanodiamonds differing in purifying methods, laser synthesis nanodiamonds and nanodiamonds made by milling. The characterization of the obtained hydrosols was conducted with Dynamic Light Scattering, Zeta potential measurements, powder XRD and TEM. According to powder XRD and TEM data ultracentrifugation also leads to a further fractionation of the primary diamond nanocrystallites in the hydrosols from 4 to 2 nm.

Model-order reduction of lumped parameter systems via fractional calculus

Science.gov (United States)

Hollkamp, John P.; Sen, Mihir; Semperlotti, Fabio

2018-04-01

This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach to the simulation of non-homogeneous systems dictates the use of numerical solutions and often imposes stringent compromises between accuracy and computational performance. Fractional calculus provides an alternative approach where complex dynamical systems can be modeled with compact fractional equations that not only can still guarantee analytical solutions, but can also enable high levels of order reduction without compromising on accuracy. Different approaches are explored in order to transform the integer order model into a reduced order fractional model able to match the dynamic response of the initial system. Analytical and numerical results show that, under certain conditions, an exact match is possible and the resulting fractional differential models have both a complex and frequency-dependent order of the differential operator. The implications of this type of approach for both model order reduction and model synthesis are discussed.

Controllability Problem of Fractional Neutral Systems: A Survey

Directory of Open Access Journals (Sweden)

Artur Babiarz

2017-01-01

Full Text Available The following article presents recent results of controllability problem of dynamical systems in infinite-dimensional space. Generally speaking, we describe selected controllability problems of fractional order systems, including approximate controllability of fractional impulsive partial neutral integrodifferential inclusions with infinite delay in Hilbert spaces, controllability of nonlinear neutral fractional impulsive differential inclusions in Banach space, controllability for a class of fractional neutral integrodifferential equations with unbounded delay, controllability of neutral fractional functional equations with impulses and infinite delay, and controllability for a class of fractional order neutral evolution control systems.

Toward lattice fractional vector calculus

International Nuclear Information System (INIS)

Tarasov, Vasily E

2014-01-01

An analog of fractional vector calculus for physical lattice models is suggested. We use an approach based on the models of three-dimensional lattices with long-range inter-particle interactions. The lattice analogs of fractional partial derivatives are represented by kernels of lattice long-range interactions, where the Fourier series transformations of these kernels have a power-law form with respect to wave vector components. In the continuum limit, these lattice partial derivatives give derivatives of non-integer order with respect to coordinates. In the three-dimensional description of the non-local continuum, the fractional differential operators have the form of fractional partial derivatives of the Riesz type. As examples of the applications of the suggested lattice fractional vector calculus, we give lattice models with long-range interactions for the fractional Maxwell equations of non-local continuous media and for the fractional generalization of the Mindlin and Aifantis continuum models of gradient elasticity. (papers)

Toward lattice fractional vector calculus

Science.gov (United States)

Tarasov, Vasily E.

2014-09-01

An analog of fractional vector calculus for physical lattice models is suggested. We use an approach based on the models of three-dimensional lattices with long-range inter-particle interactions. The lattice analogs of fractional partial derivatives are represented by kernels of lattice long-range interactions, where the Fourier series transformations of these kernels have a power-law form with respect to wave vector components. In the continuum limit, these lattice partial derivatives give derivatives of non-integer order with respect to coordinates. In the three-dimensional description of the non-local continuum, the fractional differential operators have the form of fractional partial derivatives of the Riesz type. As examples of the applications of the suggested lattice fractional vector calculus, we give lattice models with long-range interactions for the fractional Maxwell equations of non-local continuous media and for the fractional generalization of the Mindlin and Aifantis continuum models of gradient elasticity.

Fractional calculus in bioengineering, part 3.

Science.gov (United States)

Magin, Richard L

2004-01-01

Fractional calculus (integral and differential operations of noninteger order) is not often used to model biological systems. Although the basic mathematical ideas were developed long ago by the mathematicians Leibniz (1695), Liouville (1834), Riemann (1892), and others and brought to the attention of the engineering world by Oliver Heaviside in the 1890s, it was not until 1974 that the first book on the topic was published by Oldham and Spanier. Recent monographs and symposia proceedings have highlighted the application of fractional calculus in physics, continuum mechanics, signal processing, and electromagnetics, but with few examples of applications in bioengineering. This is surprising because the methods of fractional calculus, when defined as a Laplace or Fourier convolution product, are suitable for solving many problems in biomedical research. For example, early studies by Cole (1933) and Hodgkin (1946) of the electrical properties of nerve cell membranes and the propagation of electrical signals are well characterized by differential equations of fractional order. The solution involves a generalization of the exponential function to the Mittag-Leffler function, which provides a better fit to the observed cell membrane data. A parallel application of fractional derivatives to viscoelastic materials establishes, in a natural way, hereditary integrals and the power law (Nutting/Scott Blair) stress-strain relationship for modeling biomaterials. In this review, I will introduce the idea of fractional operations by following the original approach of Heaviside, demonstrate the basic operations of fractional calculus on well-behaved functions (step, ramp, pulse, sinusoid) of engineering interest, and give specific examples from electrochemistry, physics, bioengineering, and biophysics. The fractional derivative accurately describes natural phenomena that occur in such common engineering problems as heat transfer, electrode/electrolyte behavior, and sub

Sequential heavy metal extraction from dust precipitates and road sediments. Part 2. Sequential heavy metal extraction from urban dust; Sequentielle Schwermetallextraktion aus Staubniederschlaegen und Strassensedimenten. T. 2. Sequentielle Schwermetallextraktion von staedtischen Staeuben

Energy Technology Data Exchange (ETDEWEB)

Heiser, U.; Norra, S.; Stueben, D.; Wagner, M. von [Karlsruhe Univ. (T.H.) (Germany). Inst. fuer Petrographie und Geochemie

1999-03-01

For the application of our method for the sequential extraction of heavy metals from microsamples presented in part 1 (`Sequentielle Schwermetallextraktion von Mikroproben` - `Sequential Extraction of Heavy Metals from Micro Samples`) an investigation was carried out to evaluate airborne dust fallout and street sediments at two urban sites where different heavy metal immission rates occur due to traffic influence. In the street sediments the total concentrations of zinc, copper and lead was three to fivefold higher in the silt and clay fraction (<63 {mu}m) than in the particle size fraction (<1,12 mm), but showed nearly the same mobilisation behaviour. The dust samples showed equal mobilisation behaviour as the street sediments for copper and lead, while zinc was considerably more mobile in the dust samples: In extraction steps I-IV (I: mobile fraction; II: easily deliverable fraction; III: fraction bound to manganese oxides; IV: fraction bound organic to matter) zinc, copper and lead in street sediments, as well as copper and lead in dust samples, were dissolved to 40-70%, whereas about 80% of zinc in the dust samples was already dissolved in extraction step I. (orig.) [Deutsch] Mit Hilfe des in Teil 1 (`Sequentielle Schwermetallextraktion von Mikroproben`) vorgestellten Verfahrens zur sequentiellen Schwermetallextraktion von Mikroproben wurden die Mobilisierbarkeiten von Zink, Kupfer und Blei aus Staubniederschlaegen und aus der Schluff- und Tonfraktion von Strassensedimenten an zwei urbanen Standorten mit unterschiedlicher, verkehrsbedingter Schwermetallbelastung untersucht und miteinander verglichen. In Strassensedimenten wiesen Zink, Kupfer und Blei in der Schluff- und Tonfraktion drei- bis fuenffach hoehere Gesamtgehalte auf als die Korngroessenfraktion <1,12 mm, zeigten aber aehnliches Verhalten in der Mobilisierbarkeit. Bei den Staubproben war die Mobilisierbarkeit von Kupfer und Blei aehnlich wie in den Strassensedimenten, waehrend sich Zink als erheblich

An efficient technique for higher order fractional differential equation.

Science.gov (United States)

Ali, Ayyaz; Iqbal, Muhammad Asad; Ul-Hassan, Qazi Mahmood; Ahmad, Jamshad; Mohyud-Din, Syed Tauseef

2016-01-01

In this study, we establish exact solutions of fractional Kawahara equation by using the idea of [Formula: see text]-expansion method. The results of different studies show that the method is very effective and can be used as an alternative for finding exact solutions of nonlinear evolution equations (NLEEs) in mathematical physics. The solitary wave solutions are expressed by the hyperbolic, trigonometric, exponential and rational functions. Graphical representations along with the numerical data reinforce the efficacy of the used procedure. The specified idea is very effective, expedient for fractional PDEs, and could be extended to other physical problems.

Local Fractional Variational Iteration and Decomposition Methods for Wave Equation on Cantor Sets within Local Fractional Operators

Directory of Open Access Journals (Sweden)

Dumitru Baleanu

2014-01-01

Full Text Available We perform a comparison between the fractional iteration and decomposition methods applied to the wave equation on Cantor set. The operators are taken in the local sense. The results illustrate the significant features of the two methods which are both very effective and straightforward for solving the differential equations with local fractional derivative.

Applications of fractional calculus in physics

CERN Document Server

2000-01-01

Fractional calculus is a collection of relatively little-known mathematical results concerning generalizations of differentiation and integration to noninteger orders. While these results have been accumulated over centuries in various branches of mathematics, they have until recently found little appreciation or application in physics and other mathematically oriented sciences. This situation is beginning to change, and there are now a growing number of research areas in physics which employ fractional calculus.This volume provides an introduction to fractional calculus for physicists, and co

Eyewitness confidence in simultaneous and sequential lineups: a criterion shift account for sequential mistaken identification overconfidence.

Science.gov (United States)

Dobolyi, David G; Dodson, Chad S

2013-12-01

Confidence judgments for eyewitness identifications play an integral role in determining guilt during legal proceedings. Past research has shown that confidence in positive identifications is strongly associated with accuracy. Using a standard lineup recognition paradigm, we investigated accuracy using signal detection and ROC analyses, along with the tendency to choose a face with both simultaneous and sequential lineups. We replicated past findings of reduced rates of choosing with sequential as compared to simultaneous lineups, but notably found an accuracy advantage in favor of simultaneous lineups. Moreover, our analysis of the confidence-accuracy relationship revealed two key findings. First, we observed a sequential mistaken identification overconfidence effect: despite an overall reduction in false alarms, confidence for false alarms that did occur was higher with sequential lineups than with simultaneous lineups, with no differences in confidence for correct identifications. This sequential mistaken identification overconfidence effect is an expected byproduct of the use of a more conservative identification criterion with sequential than with simultaneous lineups. Second, we found a steady drop in confidence for mistaken identifications (i.e., foil identifications and false alarms) from the first to the last face in sequential lineups, whereas confidence in and accuracy of correct identifications remained relatively stable. Overall, we observed that sequential lineups are both less accurate and produce higher confidence false identifications than do simultaneous lineups. Given the increasing prominence of sequential lineups in our legal system, our data argue for increased scrutiny and possibly a wholesale reevaluation of this lineup format. PsycINFO Database Record (c) 2013 APA, all rights reserved.

INTRODUCTION OF GENERALIZED LAPLACE-FRACTIONAL MELLIN TRANSFORM

OpenAIRE

V. D. Sharma*, M. M. Thakare

2016-01-01

In present era, Fractional Integral Transform plays an important role in various fields of mathematics and Technology. Mellin transform has an many application in navigations, correlaters, in area of statistics, probability and also solving in differential equation. Fractional Mellin transform is integral part of mathematical modeling method because of its scale invariance property. The aim of this paper is to generalization of Laplace-Fractional Mellin Transform. Analyticity theore...

Dosimetric comparison of standard three-dimensional conformal radiotherapy followed by intensity-modulated radiotherapy boost schedule (sequential IMRT plan) with simultaneous integrated boost-IMRT (SIB IMRT) treatment plan in patients with localized carcinoma prostate.

Science.gov (United States)

Bansal, A; Kapoor, R; Singh, S K; Kumar, N; Oinam, A S; Sharma, S C

2012-07-01

DOSIMETERIC AND RADIOBIOLOGICAL COMPARISON OF TWO RADIATION SCHEDULES IN LOCALIZED CARCINOMA PROSTATE: Standard Three-Dimensional Conformal Radiotherapy (3DCRT) followed by Intensity Modulated Radiotherapy (IMRT) boost (sequential-IMRT) with Simultaneous Integrated Boost IMRT (SIB-IMRT). Thirty patients were enrolled. In all, the target consisted of PTV P + SV (Prostate and seminal vesicles) and PTV LN (lymph nodes) where PTV refers to planning target volume and the critical structures included: bladder, rectum and small bowel. All patients were treated with sequential-IMRT plan, but for dosimetric comparison, SIB-IMRT plan was also created. The prescription dose to PTV P + SV was 74 Gy in both strategies but with different dose per fraction, however, the dose to PTV LN was 50 Gy delivered in 25 fractions over 5 weeks for sequential-IMRT and 54 Gy delivered in 27 fractions over 5.5 weeks for SIB-IMRT. The treatment plans were compared in terms of dose-volume histograms. Also, Tumor Control Probability (TCP) and Normal Tissue Complication Probability (NTCP) obtained with the two plans were compared. The volume of rectum receiving 70 Gy or more (V > 70 Gy) was reduced to 18.23% with SIB-IMRT from 22.81% with sequential-IMRT. SIB-IMRT reduced the mean doses to both bladder and rectum by 13% and 17%, respectively, as compared to sequential-IMRT. NTCP of 0.86 ± 0.75% and 0.01 ± 0.02% for the bladder, 5.87 ± 2.58% and 4.31 ± 2.61% for the rectum and 8.83 ± 7.08% and 8.25 ± 7.98% for the bowel was seen with sequential-IMRT and SIB-IMRT plans respectively. For equal PTV coverage, SIB-IMRT markedly reduced doses to critical structures, therefore should be considered as the strategy for dose escalation. SIB-IMRT achieves lesser NTCP than sequential-IMRT.

Implementation of fractional order integrator/differentiator on field programmable gate array

OpenAIRE

K.P.S. Rana; V. Kumar; N. Mittra; N. Pramanik

2016-01-01

Concept of fractional order calculus is as old as the regular calculus. With the advent of high speed and cost effective computing power, now it is possible to model the real world control and signal processing problems using fractional order calculus. For the past two decades, applications of fractional order calculus, in system modeling, control and signal processing, have grown rapidly. This paper presents a systematic procedure for hardware implementation of the basic operators of fractio...

Physico-chemical and viscoelastic properties of high pressure homogenized lemon peel fiber fraction suspensions obtained after sequential pectin extraction

NARCIS (Netherlands)

Willemsen, K.L.D.D.; Panozzo, A.; Moelants, K.; Debon, S.J.J.; Desmet, C.; Cardinaels, R.M.; Moldenaers, P.; Wallecan, J.; Hendrickx, M.E.G.

2017-01-01

The viscoelastic properties of high pressure homogenized lemon peel cell wall fiber suspensions, obtained after sequential selective pectin extraction, were investigated in the current study. For comparison, a general pectin extraction was additionally performed on lemon peel under acid thermal

Sequential use of technetium 99m MDP and gallium 67 citrate imaging in the evaluation of painful total hip replacement

International Nuclear Information System (INIS)

Horoszowski, H.; Ganel, A.; Kamhin, M.; Zaltman, S.; Farine, I.

1980-01-01

Fourteen patients with 20 total hip joint replacements were studied for 14 painful prosthetic hips. Clinical examination, plain film radiographs and 99 Tcsup(m)-methylene diphosphonate bone scans failed to differentiate between infection and mechanical loosening of a prosthesis. Sequential use of 99 Tcsup(m)-methylene diphosphonate and 67 Ga-citrate bone scans were performed in an attempt to discover underlying infectious process. Increased focal uptake of both radiopharmaceuticals over the same hip indicated an infectious process responsible for prosthetic loosening. There were no false positive gallium examinations. Sequential use of 99 Tcsup(m)-phosphate compounds and 67 Ga-citrate is recommended for differentiation between mechanical loosening of a prosthesis and loosening of a prosthesis secondary to an infectious process. (U.K.)

Assessment of chromium biostabilization in contaminated soils using standard leaching and sequential extraction techniques

International Nuclear Information System (INIS)

Papassiopi, Nymphodora; Kontoyianni, Athina; Vaxevanidou, Katerina; Xenidis, Anthimos

2009-01-01

The iron reducing microorganism Desulfuromonas palmitatis was evaluated as potential biostabilization agent for the remediation of chromate contaminated soils. D. palmitatis were used for the treatment of soil samples artificially contaminated with Cr(VI) at two levels, i.e. 200 and 500 mg kg -1 . The efficiency of the treatment was evaluated by applying several standard extraction techniques on the soil samples before and after treatment, such as the EN12457 standard leaching test, the US EPA 3060A alkaline digestion method and the BCR sequential extraction procedure. The water soluble chromium as evaluated with the EN leaching test, was found to decrease after the biostabilization treatment from 13 to less than 0.5 mg kg -1 and from 120 to 5.6 mg kg -1 for the soil samples contaminated with 200 and 500 mg Cr(VI) per kg soil respectively. The BCR sequential extraction scheme, although not providing accurate estimates about the initial chromium speciation in contaminated soils, proved to be a useful tool for monitoring the relative changes in element partitioning, as a consequence of the stabilization treatment. After bioreduction, the percentage of chromium retained in the two least soluble BCR fractions, i.e. the 'oxidizable' and 'residual' fractions, increased from 54 and 73% to more than 96% in both soils

Occurrence and abundance of carbohydrates and amino compounds in sequentially extracted labile soil organic matter fractions.

Science.gov (United States)

This study aimed to investigate the content of carbohydrates and amino compounds in three labile fraction of soil organic matter (SOM). Soil samples were collected from two agricultural fields in southern Italy and the light fraction (LF), the 500–53-µm particulate organic matter (POM) and the mobil...

Simultaneous integrated vs. sequential boost in VMAT radiotherapy of high-grade gliomas.

Science.gov (United States)

Farzin, Mostafa; Molls, Michael; Astner, Sabrina; Rondak, Ina-Christine; Oechsner, Markus

2015-12-01

In 20 patients with high-grade gliomas, we compared two methods of planning for volumetric-modulated arc therapy (VMAT): simultaneous integrated boost (SIB) vs. sequential boost (SEB). The investigation focused on the analysis of dose distributions in the target volumes and the organs at risk (OARs). After contouring the target volumes [planning target volumes (PTVs) and boost volumes (BVs)] and OARs, SIB planning and SEB planning were performed. The SEB method consisted of two plans: in the first plan the PTV received 50 Gy in 25 fractions with a 2-Gy dose per fraction. In the second plan the BV received 10 Gy in 5 fractions with a dose per fraction of 2 Gy. The doses of both plans were summed up to show the total doses delivered. In the SIB method the PTV received 54 Gy in 30 fractions with a dose per fraction of 1.8 Gy, while the BV received 60 Gy in the same fraction number but with a dose per fraction of 2 Gy. All of the OARs showed higher doses (Dmax and Dmean) in the SEB method when compared with the SIB technique. The differences between the two methods were statistically significant in almost all of the OARs. Analysing the total doses of the target volumes we found dose distributions with similar homogeneities and comparable total doses. Our analysis shows that the SIB method offers advantages over the SEB method in terms of sparing OARs.

Precise chronology of differentiation of developing human primary dentition.

Science.gov (United States)

Hu, Xuefeng; Xu, Shan; Lin, Chensheng; Zhang, Lishan; Chen, YiPing; Zhang, Yanding

2014-02-01

While correlation of developmental stage with embryonic age of the human primary dentition has been well documented, the available information regarding the differentiation timing of the primary teeth was largely based on the observation of initial mineralization and varies significantly. In this study, we aimed to document precise differentiation timing of the developing human primary dentition. We systematically examined the expression of odontogenic differentiation markers along with the formation of mineralized tissue in each developing maxillary and mandibular teeth from human embryos with well-defined embryonic age. We show that, despite that all primary teeth initiate development at the same time, odontogenic differentiation begins in the maxillary incisors at the 15th week and in the mandibular incisors at the 16th week of gestation, followed by the canine, the first primary premolar, and the second primary premolar at a week interval sequentially. Despite that the mandibular primary incisors erupt earlier than the maxillary incisors, this distal to proximal sequential differentiation of the human primary dentition coincides in general with the sequence of tooth eruption. Our results provide an accurate chronology of odontogenic differentiation of the developing human primary dentition, which could be used as reference for future studies of human tooth development.

An Efficient Implicit FEM Scheme for Fractional-in-Space Reaction-Diffusion Equations

KAUST Repository

Burrage, Kevin

2012-01-01

Fractional differential equations are becoming increasingly used as a modelling tool for processes associated with anomalous diffusion or spatial heterogeneity. However, the presence of a fractional differential operator causes memory (time fractional) or nonlocality (space fractional) issues that impose a number of computational constraints. In this paper we develop efficient, scalable techniques for solving fractional-in-space reaction diffusion equations using the finite element method on both structured and unstructured grids via robust techniques for computing the fractional power of a matrix times a vector. Our approach is show-cased by solving the fractional Fisher and fractional Allen-Cahn reaction-diffusion equations in two and three spatial dimensions, and analyzing the speed of the traveling wave and size of the interface in terms of the fractional power of the underlying Laplacian operator. © 2012 Society for Industrial and Applied Mathematics.

Riemann-Liouville integrals of fractional order and extended KP hierarchy

International Nuclear Information System (INIS)

Kamata, Masaru; Nakamula, Atsushi

2002-01-01

An attempt to formulate the extensions of the KP hierarchy by introducing fractional-order pseudo-differential operators is given. In the case of the extension with the half-order pseudo-differential operators, a system analogous to the supersymmetric extensions of the KP hierarchy is obtained. Unlike the supersymmetric extensions, no Grassmannian variable appears in the hierarchy considered here. More general hierarchies constructed by the 1/Nth-order pseudo-differential operators, their integrability and the reduction procedure are also investigated. In addition to finding the new extensions of the KP hierarchy, a brief introduction to the Riemann-Liouville integral is provided to yield a candidate for the fractional-order pseudo-differential operators

Chemical fractionation of heavy metals in a soil amended with repeated sewage sludge application

International Nuclear Information System (INIS)

Walter, I.; Cuevas, G.

1999-01-01

A sequential extraction method (KNO 3 , NaOH, Na 2 -EDTA, HNO 3 ) was used to determine the soil fraction of Zn, Cd, Cu, Ni, Pb, and Cr in different plots treated with sewage sludges. The sludges were applied to cropland from 1983 to 1991. Soil samples were collected after the 1st and 5th-year of the last sludge application. Sludge applications increased the INOR-fraction for Zn, Cd, and Cu. Cu was the only element found in the EXCH-fraction. Pb and Cr were found mainly in the RES-fraction. Ni was found in the INOR and OM-fractions. All the metals increased in the more resistant fractions. Sewage sludge applications changed the metals distribution of the soil and this effect has continued for at least 5 years. (Copyright (c) 1999 Elsevier Science B.V., Amsterdam. All rights reserved.)

Differential branching fraction and angular moments analysis of the decay $B^0 \\to K^+ \\pi^- \\mu^+ \\mu^-$ in the $K^*_{0,2}(1430)^0$ region

CERN Document Server

Aaij, Roel; Adinolfi, Marco; Ajaltouni, Ziad; Akar, Simon; Albrecht, Johannes; Alessio, Federico; Alexander, Michael; Ali, Suvayu; Alkhazov, Georgy; Alvarez Cartelle, Paula; Alves Jr, Antonio Augusto; Amato, Sandra; Amerio, Silvia; Amhis, Yasmine; An, Liupan; Anderlini, Lucio; Andreassi, Guido; Andreotti, Mirco; Andrews, Jason; Appleby, Robert; Archilli, Flavio; d'Argent, Philippe; Arnau Romeu, Joan; Artamonov, Alexander; Artuso, Marina; Aslanides, Elie; Auriemma, Giulio; Baalouch, Marouen; Babuschkin, Igor; Bachmann, Sebastian; Back, John; Badalov, Alexey; Baesso, Clarissa; Baldini, Wander; Barlow, Roger; Barschel, Colin; Barsuk, Sergey; Barter, William; Baszczyk, Mateusz; Batozskaya, Varvara; Batsukh, Baasansuren; Battista, Vincenzo; Bay, Aurelio; Beaucourt, Leo; Beddow, John; Bedeschi, Franco; Bediaga, Ignacio; Bel, Lennaert; Bellee, Violaine; Belloli, Nicoletta; Belous, Konstantin; Belyaev, Ivan; Ben-Haim, Eli; Bencivenni, Giovanni; Benson, Sean; Benton, Jack; Berezhnoy, Alexander; Bernet, Roland; Bertolin, Alessandro; Betti, Federico; Bettler, Marc-Olivier; van Beuzekom, Martinus; Bezshyiko, Iaroslava; Bifani, Simone; Billoir, Pierre; Bird, Thomas; Birnkraut, Alex; Bitadze, Alexander; Bizzeti, Andrea; Blake, Thomas; Blanc, Frederic; Blouw, Johan; Blusk, Steven; Bocci, Valerio; Boettcher, Thomas; Bondar, Alexander; Bondar, Nikolay; Bonivento, Walter; Borgheresi, Alessio; Borghi, Silvia; Borisyak, Maxim; Borsato, Martino; Bossu, Francesco; Boubdir, Meriem; Bowcock, Themistocles; Bowen, Espen Eie; Bozzi, Concezio; Braun, Svende; Britsch, Markward; Britton, Thomas; Brodzicka, Jolanta; Buchanan, Emma; Burr, Christopher; Bursche, Albert; Buytaert, Jan; Cadeddu, Sandro; Calabrese, Roberto; Calvi, Marta; Calvo Gomez, Miriam; Camboni, Alessandro; Campana, Pierluigi; Campora Perez, Daniel; Campora Perez, Daniel Hugo; Capriotti, Lorenzo; Carbone, Angelo; Carboni, Giovanni; Cardinale, Roberta; Cardini, Alessandro; Carniti, Paolo; Carson, Laurence; Carvalho Akiba, Kazuyoshi; Casse, Gianluigi; Cassina, Lorenzo; Castillo Garcia, Lucia; Cattaneo, Marco; Cauet, Christophe; Cavallero, Giovanni; Cenci, Riccardo; Charles, Matthew; Charpentier, Philippe; Chatzikonstantinidis, Georgios; Chefdeville, Maximilien; Chen, Shanzhen; Cheung, Shu-Faye; Chobanova, Veronika; Chrzaszcz, Marcin; Cid Vidal, Xabier; Ciezarek, Gregory; Clarke, Peter; Clemencic, Marco; Cliff, Harry; Closier, Joel; Coco, Victor; Cogan, Julien; Cogneras, Eric; Cogoni, Violetta; Cojocariu, Lucian; Collazuol, Gianmaria; Collins, Paula; Comerma-Montells, Albert; Contu, Andrea; Cook, Andrew; Coquereau, Samuel; Corti, Gloria; Corvo, Marco; Costa Sobral, Cayo Mar; Couturier, Benjamin; Cowan, Greig; Craik, Daniel Charles; Crocombe, Andrew; Cruz Torres, Melissa Maria; Cunliffe, Samuel; Currie, Robert; D'Ambrosio, Carmelo; Dall'Occo, Elena; Dalseno, Jeremy; David, Pieter; Davis, Adam; De Aguiar Francisco, Oscar; De Bruyn, Kristof; De Capua, Stefano; De Cian, Michel; De Miranda, Jussara; De Paula, Leandro; De Serio, Marilisa; De Simone, Patrizia; Dean, Cameron Thomas; Decamp, Daniel; Deckenhoff, Mirko; Del Buono, Luigi; Demmer, Moritz; Derkach, Denis; Deschamps, Olivier; Dettori, Francesco; Dey, Biplab; Di Canto, Angelo; Dijkstra, Hans; Dordei, Francesca; Dorigo, Mirco; Dosil Suárez, Alvaro; Dovbnya, Anatoliy; Dreimanis, Karlis; Dufour, Laurent; Dujany, Giulio; Dungs, Kevin; Durante, Paolo; Dzhelyadin, Rustem; Dziurda, Agnieszka; Dzyuba, Alexey; Déléage, Nicolas; Easo, Sajan; Ebert, Marcus; Egede, Ulrik; Egorychev, Victor; Eidelman, Semen; Eisenhardt, Stephan; Eitschberger, Ulrich; Ekelhof, Robert; Eklund, Lars; Elsasser, Christian; Ely, Scott; Esen, Sevda; Evans, Hannah Mary; Evans, Timothy; Falabella, Antonio; Farley, Nathanael; Farry, Stephen; Fay, Robert; Fazzini, Davide; Ferguson, Dianne; Fernandez Albor, Victor; Fernandez Prieto, Antonio; Ferrari, Fabio; Ferreira Rodrigues, Fernando; Ferro-Luzzi, Massimiliano; Filippov, Sergey; Fini, Rosa Anna; Fiore, Marco; Fiorini, Massimiliano; Firlej, Miroslaw; Fitzpatrick, Conor; Fiutowski, Tomasz; Fleuret, Frederic; Fohl, Klaus; Fontana, Marianna; Fontanelli, Flavio; Forshaw, Dean Charles; Forty, Roger; Franco Lima, Vinicius; Frank, Markus; Frei, Christoph; Fu, Jinlin; Furfaro, Emiliano; Färber, Christian; Gallas Torreira, Abraham; Galli, Domenico; Gallorini, Stefano; Gambetta, Silvia; Gandelman, Miriam; Gandini, Paolo; Gao, Yuanning; Garcia Martin, Luis Miguel; García Pardiñas, Julián; Garra Tico, Jordi; Garrido, Lluis; Garsed, Philip John; Gascon, David; Gaspar, Clara; Gavardi, Laura; Gazzoni, Giulio; Gerick, David; Gersabeck, Evelina; Gersabeck, Marco; Gershon, Timothy; Ghez, Philippe; Gianì, Sebastiana; Gibson, Valerie; Girard, Olivier Göran; Giubega, Lavinia-Helena; Gizdov, Konstantin; Gligorov, V.V.; Golubkov, Dmitry; Golutvin, Andrey; Gomes, Alvaro; Gorelov, Igor Vladimirovich; Gotti, Claudio; Grabalosa Gándara, Marc; Graciani Diaz, Ricardo; Granado Cardoso, Luis Alberto; Graugés, Eugeni; Graverini, Elena; Graziani, Giacomo; Grecu, Alexandru; Griffith, Peter; Grillo, Lucia; Gruberg Cazon, Barak Raimond; Grünberg, Oliver; Gushchin, Evgeny; Guz, Yury; Gys, Thierry; Göbel, Carla; Hadavizadeh, Thomas; Hadjivasiliou, Christos; Haefeli, Guido; Haen, Christophe; Haines, Susan; Hall, Samuel; Hamilton, Brian; Han, Xiaoxue; Hansmann-Menzemer, Stephanie; Harnew, Neville; Harnew, Samuel; Harrison, Jonathan; Hatch, Mark; He, Jibo; Head, Timothy; Heister, Arno; Hennessy, Karol; Henrard, Pierre; Henry, Louis; Hernando Morata, Jose Angel; van Herwijnen, Eric; Heß, Miriam; Hicheur, Adlène; Hill, Donal; Hombach, Christoph; Hopchev, P H; Hulsbergen, Wouter; Humair, Thibaud; Hushchyn, Mikhail; Hussain, Nazim; Hutchcroft, David; Idzik, Marek; Ilten, Philip; Jacobsson, Richard; Jaeger, Andreas; Jalocha, Pawel; Jans, Eddy; Jawahery, Abolhassan; John, Malcolm; Johnson, Daniel; Jones, Christopher; Joram, Christian; Jost, Beat; Jurik, Nathan; Kandybei, Sergii; Kanso, Walaa; Karacson, Matthias; Kariuki, James Mwangi; Karodia, Sarah; Kecke, Matthieu; Kelsey, Matthew; Kenyon, Ian; Kenzie, Matthew; Ketel, Tjeerd; Khairullin, Egor; Khanji, Basem; Khurewathanakul, Chitsanu; Kirn, Thomas; Klaver, Suzanne; Klimaszewski, Konrad; Koliiev, Serhii; Kolpin, Michael; Komarov, Ilya; Koopman, Rose; Koppenburg, Patrick; Kozachuk, Anastasiia; Kozeiha, Mohamad; Kravchuk, Leonid; Kreplin, Katharina; Kreps, Michal; Krokovny, Pavel; Kruse, Florian; Krzemien, Wojciech; Kucewicz, Wojciech; Kucharczyk, Marcin; Kudryavtsev, Vasily; Kuonen, Axel Kevin; Kurek, Krzysztof; Kvaratskheliya, Tengiz; Lacarrere, Daniel; Lafferty, George; Lai, Adriano; Lambert, Dean; Lanfranchi, Gaia; Langenbruch, Christoph; Langhans, Benedikt; Latham, Thomas; Lazzeroni, Cristina; Le Gac, Renaud; van Leerdam, Jeroen; Lees, Jean-Pierre; Leflat, Alexander; Lefrançois, Jacques; Lefèvre, Regis; Lemaitre, Florian; Lemos Cid, Edgar; Leroy, Olivier; Lesiak, Tadeusz; Leverington, Blake; Li, Yiming; Likhomanenko, Tatiana; Lindner, Rolf; Linn, Christian; Lionetto, Federica; Liu, Bo; Liu, Xuesong; Loh, David; Longstaff, Iain; Lopes, Jose; Lucchesi, Donatella; Lucio Martinez, Miriam; Luo, Haofei; Lupato, Anna; Luppi, Eleonora; Lupton, Oliver; Lusiani, Alberto; Lyu, Xiao-Rui; Machefert, Frederic; Maciuc, Florin; Maev, Oleg; Maguire, Kevin; Malde, Sneha; Malinin, Alexander; Maltsev, Timofei; Manca, Giulia; Mancinelli, Giampiero; Manning, Peter Michael; Maratas, Jan; Marchand, Jean François; Marconi, Umberto; Marin Benito, Carla; Marino, Pietro; Marks, Jörg; Martellotti, Giuseppe; Martin, Morgan; Martinelli, Maurizio; Martinez Santos, Diego; Martinez Vidal, Fernando; Martins Tostes, Danielle; Massacrier, Laure Marie; Massafferri, André; Matev, Rosen; Mathad, Abhijit; Mathe, Zoltan; Matteuzzi, Clara; Mauri, Andrea; Maurin, Brice; Mazurov, Alexander; McCann, Michael; McCarthy, James; McNab, Andrew; McNulty, Ronan; Meadows, Brian; Meier, Frank; Meissner, Marco; Melnychuk, Dmytro; Merk, Marcel; Merli, Andrea; Michielin, Emanuele; Milanes, Diego Alejandro; Minard, Marie-Noelle; Mitzel, Dominik Stefan; Mogini, Andrea; Molina Rodriguez, Josue; Monroy, Ignacio Alberto; Monteil, Stephane; Morandin, Mauro; Morawski, Piotr; Mordà, Alessandro; Morello, Michael Joseph; Moron, Jakub; Morris, Adam Benjamin; Mountain, Raymond; Muheim, Franz; Mulder, Mick; Mussini, Manuel; Müller, Dominik; Müller, Janine; Müller, Katharina; Müller, Vanessa; Naik, Paras; Nakada, Tatsuya; Nandakumar, Raja; Nandi, Anita; Nasteva, Irina; Needham, Matthew; Neri, Nicola; Neubert, Sebastian; Neufeld, Niko; Neuner, Max; Nguyen, Anh Duc; Nguyen-Mau, Chung; Nieswand, Simon; Niet, Ramon; Nikitin, Nikolay; Nikodem, Thomas; Novoselov, Alexey; O'Hanlon, Daniel Patrick; Oblakowska-Mucha, Agnieszka; Obraztsov, Vladimir; Ogilvy, Stephen; Oldeman, Rudolf; Onderwater, Gerco; Otalora Goicochea, Juan Martin; Otto, Adam; Owen, Patrick; Oyanguren, Maria Aranzazu; Pais, Preema Rennee; Palano, Antimo; Palombo, Fernando; Palutan, Matteo; Panman, Jacob; Papanestis, Antonios; Pappagallo, Marco; Pappalardo, Luciano; Parker, William; Parkes, Christopher; Passaleva, Giovanni; Pastore, Alessandra; Patel, Girish; Patel, Mitesh; Patrignani, Claudia; Pearce, Alex; Pellegrino, Antonio; Penso, Gianni; Pepe Altarelli, Monica; Perazzini, Stefano; Perret, Pascal; Pescatore, Luca; Petridis, Konstantinos; Petrolini, Alessandro; Petrov, Aleksandr; Petruzzo, Marco; Picatoste Olloqui, Eduardo; Pietrzyk, Boleslaw; Pikies, Malgorzata; Pinci, Davide; Pistone, Alessandro; Piucci, Alessio; Playfer, Stephen; Plo Casasus, Maximo; Poikela, Tuomas; Polci, Francesco; Poluektov, Anton; Polyakov, Ivan; Polycarpo, Erica; Pomery, Gabriela Johanna; Popov, Alexander; Popov, Dmitry; Popovici, Bogdan; Poslavskii, Stanislav; Potterat, Cédric; Price, Eugenia; Price, Joseph David; Prisciandaro, Jessica; Pritchard, Adrian; Prouve, Claire; Pugatch, Valery; Puig Navarro, Albert; Punzi, Giovanni; Qian, Wenbin; Quagliani, Renato; Rachwal, Bartolomiej; Rademacker, Jonas; Rama, Matteo; Ramos Pernas, Miguel; Rangel, Murilo; Raniuk, Iurii; Raven, Gerhard; Redi, Federico; Reichert, Stefanie; dos Reis, Alberto; Remon Alepuz, Clara; Renaudin, Victor; Ricciardi, Stefania; Richards, Sophie; Rihl, Mariana; Rinnert, Kurt; Rives Molina, Vicente; Robbe, Patrick; Rodrigues, Ana Barbara; Rodrigues, Eduardo; Rodriguez Lopez, Jairo Alexis; Rodriguez Perez, Pablo; Rogozhnikov, Alexey; Roiser, Stefan; Romanovskiy, Vladimir; Romero Vidal, Antonio; Ronayne, John William; Rotondo, Marcello; Rudolph, Matthew Scott; Ruf, Thomas; Ruiz Valls, Pablo; Saborido Silva, Juan Jose; Sadykhov, Elnur; Sagidova, Naylya; Saitta, Biagio; Salustino Guimaraes, Valdir; Sanchez Mayordomo, Carlos; Sanmartin Sedes, Brais; Santacesaria, Roberta; Santamarina Rios, Cibran; Santimaria, Marco; Santovetti, Emanuele; Sarti, Alessio; Satriano, Celestina; Satta, Alessia; Saunders, Daniel Martin; Savrina, Darya; Schael, Stefan; Schellenberg, Margarete; Schiller, Manuel; Schindler, Heinrich; Schlupp, Maximilian; Schmelling, Michael; Schmelzer, Timon; Schmidt, Burkhard; Schneider, Olivier; Schopper, Andreas; Schubert, Konstantin; Schubiger, Maxime; Schune, Marie Helene; Schwemmer, Rainer; Sciascia, Barbara; Sciubba, Adalberto; Semennikov, Alexander; Sergi, Antonino; Serra, Nicola; Serrano, Justine; Sestini, Lorenzo; Seyfert, Paul; Shapkin, Mikhail; Shapoval, Illya; Shcheglov, Yury; Shears, Tara; Shekhtman, Lev; Shevchenko, Vladimir; Shires, Alexander; Siddi, Benedetto Gianluca; Silva Coutinho, Rafael; Silva de Oliveira, Luiz Gustavo; Simi, Gabriele; Simone, Saverio; Sirendi, Marek; Skidmore, Nicola; Skwarnicki, Tomasz; Smith, Eluned; Smith, Iwan Thomas; Smith, Jackson; Smith, Mark; Snoek, Hella; Sokoloff, Michael; Soler, Paul; Souza, Daniel; Souza De Paula, Bruno; Spaan, Bernhard; Spradlin, Patrick; Sridharan, Srikanth; Stagni, Federico; Stahl, Marian; Stahl, Sascha; Stefko, Pavol; Stefkova, Slavorima; Steinkamp, Olaf; Stemmle, Simon; Stenyakin, Oleg; Stevenson, Scott; Stoica, Sabin; Stone, Sheldon; Storaci, Barbara; Stracka, Simone; Straticiuc, Mihai; Straumann, Ulrich; Sun, Liang; Sutcliffe, William; Swientek, Krzysztof; Syropoulos, Vasileios; Szczekowski, Marek; Szumlak, Tomasz; T'Jampens, Stephane; Tayduganov, Andrey; Tekampe, Tobias; Tellarini, Giulia; Teubert, Frederic; Thomas, Christopher; Thomas, Eric; van Tilburg, Jeroen; Tisserand, Vincent; Tobin, Mark; Tolk, Siim; Tomassetti, Luca; Tonelli, Diego; Topp-Joergensen, Stig; Toriello, Francis; Tournefier, Edwige; Tourneur, Stephane; Trabelsi, Karim; Traill, Murdo; Tran, Minh Tâm; Tresch, Marco; Trisovic, Ana; Tsaregorodtsev, Andrei; Tsopelas, Panagiotis; Tully, Alison; Tuning, Niels; Ukleja, Artur; Ustyuzhanin, Andrey; Uwer, Ulrich; Vacca, Claudia; Vagnoni, Vincenzo; Valassi, Andrea; Valat, Sebastien; Valenti, Giovanni; Vallier, Alexis; Vazquez Gomez, Ricardo; Vazquez Regueiro, Pablo; Vecchi, Stefania; van Veghel, Maarten; Velthuis, Jaap; Veltri, Michele; Veneziano, Giovanni; Venkateswaran, Aravindhan; Vernet, Maxime; Vesterinen, Mika; Viaud, Benoit; Vieira, Daniel; Vieites Diaz, Maria; Vilasis-Cardona, Xavier; Volkov, Vladimir; Vollhardt, Achim; Voneki, Balazs; Vorobyev, Alexey; Vorobyev, Vitaly; Voß, Christian; de Vries, Jacco; Vázquez Sierra, Carlos; Waldi, Roland; Wallace, Charlotte; Wallace, Ronan; Walsh, John; Wang, Jianchun; Ward, David; Wark, Heather Mckenzie; Watson, Nigel; Websdale, David; Weiden, Andreas; Whitehead, Mark; Wicht, Jean; Wilkinson, Guy; Wilkinson, Michael; Williams, Mark Richard James; Williams, Matthew; Williams, Mike; Williams, Timothy; Wilson, Fergus; Wimberley, Jack; Wishahi, Julian; Wislicki, Wojciech; Witek, Mariusz; Wormser, Guy; Wotton, Stephen; Wraight, Kenneth; Wright, Simon; Wyllie, Kenneth; Xie, Yuehong; Xing, Zhou; Xu, Zhirui; Yang, Zhenwei; Yin, Hang; Yu, Jiesheng; Yuan, Xuhao; Yushchenko, Oleg; Zangoli, Maria; Zarebski, Kristian Alexander; Zavertyaev, Mikhail; Zhang, Liming; Zhang, Yanxi; Zhang, Yu; Zhelezov, Alexey; Zheng, Yangheng; Zhokhov, Anatoly; Zhu, Xianglei; Zhukov, Valery; Zucchelli, Stefano

2016-12-15

Measurements of the differential branching fraction and angular moments of the decay $B^0 \\to K^+ \\pi^- \\mu^+ \\mu^-$ in the $K^*_{0,2}(1430)^0$ in the $K^+\\pi^-$ invariant mass range $1330 < m (K^+ \\pi^-) <1530~ \\text{MeV}/c^2$ are presented. Proton-proton collision data are used, corresponding to an integrated luminosity of 3 fb$^{-1}$ collected by the LHCb experiment. Differential branching fraction measurements are reported in five bins of the invariant mass squared of the dimuon system, $q^2$, between 0.1 and 8.0 $\\text{GeV}^2/c^4$. For the first time, an angular analysis sensitive to the S-, P- and D-wave contributions of this rare decay is performed. The set of 40 normalised angular moments describing the decay is presented for the $q^2$ range $1.1-6.0 \\text{GeV}^2/c^4$.

Sequential extraction applied to Peruibe black mud, SP, Brazil

International Nuclear Information System (INIS)

Torrecilha, Jefferson Koyaishi

2014-01-01

The Peruibe Black mud is used in therapeutic treatments such as psoriasis, peripheral dermatitis, acne and seborrhoea, as well as in the treatment of myalgia, arthritis, rheumatism and non-articular processes. Likewise other medicinal clays, it may not be free from possible adverse health effects due to possible hazardous minerals leading to respiratory system occurrences and other effects, caused by the presence of toxic elements. Once used for therapeutic purposes, any given material should be fully characterized and thus samples of Peruibe black mud were analyzed to determine physical and chemical properties: moisture content, organic matter and loss on ignition; pH, particle size, cation exchange capacity and swelling index. The elemental composition was determined by Neutron Activation Analysis, Atomic Absorption Graphite Furnace and X-ray fluorescence; the mineralogical composition was determined by X-ray diffraction. Another tool widely used to evaluate the behavior of trace elements, in various environmental matrices, is the sequential extraction. Thus, a sequential extraction procedure was applied to fractionate the mud in specific geochemical forms and verify how and how much of the elements may be contained in it. Considering the several sequential extraction procedures, BCR-701 method (Community Bureau of Reference) was used since it is considered the most reproducible among them. A simple extraction with an artificial sweat was, also, applied in order to verify which components are potentially available for absorption by the patient skin during the topical treatment. The results indicated that the mud is basically composed by a silty-clay material, rich in organic matter and with good cation exchange capacity. There were no significant variations in mineralogy and elemental composition of both, in natura and mature mud forms. The analysis by sequential extraction and by simple extraction indicated that the elements possibly available in larger

Analysis of a time fractional wave-like equation with the homotopy analysis method

International Nuclear Information System (INIS)

Xu Hang; Cang Jie

2008-01-01

The time fractional wave-like differential equation with a variable coefficient is studied analytically. By using a simple transformation, the governing equation is reduced to two fractional ordinary differential equations. Then the homotopy analysis method is employed to derive the solutions of these equations. The accurate series solutions are obtained. Especially, when h f =h g =-1, these solutions are exactly the same as those results given by the Adomian decomposition method. The present work shows the validity and great potential of the homotopy analysis method for solving nonlinear fractional differential equations. The basic idea described in this Letter is expected to be further employed to solve other similar nonlinear problems in fractional calculus

Multistrain models predict sequential multidrug treatment strategies to result in less antimicrobial resistance than combination treatment

DEFF Research Database (Denmark)

Ahmad, Amais; Zachariasen, Camilla; Christiansen, Lasse Engbo

2016-01-01

Background: Combination treatment is increasingly used to fight infections caused by bacteria resistant to two or more antimicrobials. While multiple studies have evaluated treatment strategies to minimize the emergence of resistant strains for single antimicrobial treatment, fewer studies have...... the sensitive fraction of the commensal flora.Growth parameters for competing bacterial strains were estimated from the combined in vitro pharmacodynamic effect of two antimicrobials using the relationship between concentration and net bacterial growth rate. Predictions of in vivo bacterial growth were...... (how frequently antibiotics are alternated in a sequential treatment) of the two drugs was dependent upon the order in which the two drugs were used.Conclusion: Sequential treatment was more effective in preventing the growth of resistant strains when compared to the combination treatment. The cycling...

Fractional neutron point kinetics equations for nuclear reactor dynamics

International Nuclear Information System (INIS)

Espinosa-Paredes, Gilberto; Polo-Labarrios, Marco-A.; Espinosa-Martinez, Erick-G.; Valle-Gallegos, Edmundo del

2011-01-01

The fractional point-neutron kinetics model for the dynamic behavior in a nuclear reactor is derived and analyzed in this paper. The fractional model retains the main dynamic characteristics of the neutron motion in which the relaxation time associated with a rapid variation in the neutron flux contains a fractional order, acting as exponent of the relaxation time, to obtain the best representation of a nuclear reactor dynamics. The physical interpretation of the fractional order is related with non-Fickian effects from the neutron diffusion equation point of view. The numerical approximation to the solution of the fractional neutron point kinetics model, which can be represented as a multi-term high-order linear fractional differential equation, is calculated by reducing the problem to a system of ordinary and fractional differential equations. The numerical stability of the fractional scheme is investigated in this work. Results for neutron dynamic behavior for both positive and negative reactivity and for different values of fractional order are shown and compared with the classic neutron point kinetic equations. Additionally, a related review with the neutron point kinetics equations is presented, which encompasses papers written in English about this research topic (as well as some books and technical reports) published since 1940 up to 2010.

Study of Cu and Pb partitioning in mine tailings using the Tessier sequential extraction scheme

Energy Technology Data Exchange (ETDEWEB)

Andrei, Mariana Lucia, E-mail: marianaluciaandrei@yahoo.com [National Institute for Research and Development of Isotopic and Molecular Technologies, 65-103 Donath, 400293 Cluj-Napoca (Romania); Babes-Bolyai University, Environmental Science and Engineering Faculty, 30 Fantanele, 400294, Cluj-Napoca (Romania); Senila, Marin; Hoaghia, Maria Alexandra; Levei, Erika-Andrea [INCDO-INOE 2000, Research Institute for Analytical Instrumentation, 67 Donath, 400293, Cluj-Napoca (Romania); Borodi, Gheorghe [National Institute for Research and Development of Isotopic and Molecular Technologies, 65-103 Donath, 400293 Cluj-Napoca (Romania)

2015-12-23

The Cu and Pb partitioning in nonferrous mine tailings was investigated using the Tessier sequential extraction scheme. The contents of Cu and Pb found in the five operationally defined fractions were determined by inductively coupled plasma optical emission spectrometry. The results showed different partitioning patterns for Cu and Pb in the studied tailings. The total Cu and Pb contents were higher in tailings from Brazesti than in those from Saliste, while the Cu contents in the first two fractions considered as mobile were comparable and the content of mobile Pb was the highest in Brazesti tailings. In the tailings from Saliste about 30% of Cu and 3% of Pb were found in exchangeable fraction, while in those from Brazesti no metals were found in the exchangeable fraction, but the percent of Cu and Pb found in the bound to carbonate fraction were high (20% and 26%, respectively). The highest Pb content was found in the residual fraction in Saliste tailings and in bound to Fe and Mn oxides fraction in Brazesti tailings, while the highest Cu content was found in the fraction bound to organic matter in Saliste tailings and in the residual fraction in Brazesti tailings. In case of tailings of Brazesti medium environmental risk was found both for Pb and Cu, while in case of Saliste tailings low risk for Pb and high risk for Cu were found.

Study of Cu and Pb partitioning in mine tailings using the Tessier sequential extraction scheme

International Nuclear Information System (INIS)

Andrei, Mariana Lucia; Senila, Marin; Hoaghia, Maria Alexandra; Levei, Erika-Andrea; Borodi, Gheorghe

2015-01-01

The Cu and Pb partitioning in nonferrous mine tailings was investigated using the Tessier sequential extraction scheme. The contents of Cu and Pb found in the five operationally defined fractions were determined by inductively coupled plasma optical emission spectrometry. The results showed different partitioning patterns for Cu and Pb in the studied tailings. The total Cu and Pb contents were higher in tailings from Brazesti than in those from Saliste, while the Cu contents in the first two fractions considered as mobile were comparable and the content of mobile Pb was the highest in Brazesti tailings. In the tailings from Saliste about 30% of Cu and 3% of Pb were found in exchangeable fraction, while in those from Brazesti no metals were found in the exchangeable fraction, but the percent of Cu and Pb found in the bound to carbonate fraction were high (20% and 26%, respectively). The highest Pb content was found in the residual fraction in Saliste tailings and in bound to Fe and Mn oxides fraction in Brazesti tailings, while the highest Cu content was found in the fraction bound to organic matter in Saliste tailings and in the residual fraction in Brazesti tailings. In case of tailings of Brazesti medium environmental risk was found both for Pb and Cu, while in case of Saliste tailings low risk for Pb and high risk for Cu were found

Assessment of cardiac performance with quantitative radionuclide angiocardiography: sequential left ventricular ejection fraction, normalized left ventricular ejection rate, and regional wall motion

International Nuclear Information System (INIS)

Marshall, R.C.; Berger, H.J.; Costin, J.C.; Freedman, G.S.; Wolberg, J.; Cohen, L.S.; Gotischalk, A.; Zaret, B.L.

1977-01-01

Sequential quantitative first pass radionuclide angiocardiograms (RA) were used to measure left ventricular ejection fraction (LVEF) and left ventricular ejection rate (LVER), and to assess regional wall motion (RWM) in the anterior (ANT) and left anterior oblique (LAO) positions. Studies were obtained with a computerized multicrystal scintillation camera suitable for acquiring high count-rate data. Background was determined in a new fashion by selecting frames temporally from the left ventricular region of interest time-activity curve. A ''representative'' cardiac cycle was formed by summing together counts over three to six cardiac cycles. From this background corrected, high count-rate ''representative''cardiac cycle, LVEF, LVER, and RWM were determined. In 22 patients with normal sinus rhythm in the absence of significant valvular regurgitation, RA LVEF correlated well with that measured by contrast angiography (r = 0.95). LVER correlated well with LVEF measured at contrast angiography (r = 0.90) and allowed complete separation of those with normal (LVER = 3.4 +- 0.17 sec -1 ) and abnormal (LVER = 1.22 +- 0.11 sec -1 ) (P < 0.001) left ventricular performance. This separation was independent of background. Isoproterenol infusion in five normal subjects caused LVER to increase by 81 +- 17% while LVEF increased by 10 +- 2.0%. RWM was correctly defined in 21/22 patients and 89% of left ventricular segments with abnormal wall motion

Fractional virus epidemic model on financial networks

Directory of Open Access Journals (Sweden)

Balci Mehmet Ali

2016-01-01

Full Text Available In this study, we present an epidemic model that characterizes the behavior of a financial network of globally operating stock markets. Since the long time series have a global memory effect, we represent our model by using the fractional calculus. This model operates on a network, where vertices are the stock markets and edges are constructed by the correlation distances. Thereafter, we find an analytical solution to commensurate system and use the well-known differential transform method to obtain the solution of incommensurate system of fractional differential equations. Our findings are confirmed and complemented by the data set of the relevant stock markets between 2006 and 2016. Rather than the hypothetical values, we use the Hurst Exponent of each time series to approximate the fraction size and graph theoretical concepts to obtain the variables.

Enhancement of sequential zymography technique for the detection of thermophilic lipases and proteases.

Science.gov (United States)

Wilkesman, Jeff; Hernández, Zully; Fernández, Marleny; Contreras, Lellys M; Kurz, Liliana

2014-05-01

Analysis of lipases and proteases present in cell-free fractions of thermophilic Bacillus sp. cultures were performed in an enhanced sequential zymography method. After the PAGE run, the gel was electrotransferred to another polyacrylamide gel containing a mixture of glycerol tributyrate, olive oil and gelatin. After transference, this substrate-mix gel was incubated for lipase detection, until bands appeared, and later stained with CBB for protease detection. Assets are, besides detecting two enzymes on a single gel, time and material saving.

Remarks on sequential designs in risk assessment

International Nuclear Information System (INIS)

Seidenfeld, T.

1982-01-01

The special merits of sequential designs are reviewed in light of particular challenges that attend risk assessment for human population. The kinds of ''statistical inference'' are distinguished and the problem of design which is pursued is the clash between Neyman-Pearson and Bayesian programs of sequential design. The value of sequential designs is discussed and the Neyman-Pearson vs. Bayesian sequential designs are probed in particular. Finally, warnings with sequential designs are considered, especially in relation to utilitarianism

Generalization of Fuzzy Laplace Transforms of Fuzzy Fractional Derivatives about the General Fractional Order n-1<β

Directory of Open Access Journals (Sweden)

Amal Khalaf Haydar

2016-01-01

Full Text Available The main aim in this paper is to use all the possible arrangements of objects such that r1 of them are equal to 1 and r2 (the others of them are equal to 2, in order to generalize the definitions of Riemann-Liouville and Caputo fractional derivatives (about order 0<βfractional derivatives about the general fractional order n-1<βdifferentiability. Some fuzzy fractional initial value problems (FFIVPs are solved using the above two generalizations.

Differential branching fraction and angular analysis of the decay $B^{0} \\rightarrow K^{*0} \\mu^{+}\\mu^{-}$

CERN Document Server

Aaij, R.; Adeva, B.; Adinolfi, M.; Adrover, C.; Affolder, A.; Ajaltouni, Z.; Albrecht, J.; Alessio, F.; Alexander, M.; Ali, S.; Alkhazov, G.; Alvarez Cartelle, P.; Alves Jr, A.A.; Amato, S.; Amerio, S.; Amhis, Y.; Anderlini, L.; Anderson, J.; Andreassen, R.; Appleby, R.B.; Aquines Gutierrez, O.; Archilli, F.; Artamonov, A.; Artuso, M.; Aslanides, E.; Auriemma, G.; Bachmann, S.; Back, J.J.; Baesso, C.; Balagura, V.; Baldini, W.; Barlow, R.J.; Barschel, C.; Barsuk, S.; Barter, W.; Bauer, Th.; Bay, A.; Beddow, J.; Bedeschi, F.; Bediaga, I.; Belogurov, S.; Belous, K.; Belyaev, I.; Ben-Haim, E.; Bencivenni, G.; Benson, S.; Benton, J.; Berezhnoy, A.; Bernet, R.; Bettler, M.O.; van Beuzekom, M.; Bien, A.; Bifani, S.; Bird, T.; Bizzeti, A.; Bjornstad, P.M.; Blake, T.; Blanc, F.; Blouw, J.; Blusk, S.; Bocci, V.; Bondar, A.; Bondar, N.; Bonivento, W.; Borghi, S.; Borgia, A.; Bowcock, T.J.V.; Bowen, E.; Bozzi, C.; Brambach, T.; van den Brand, J.; Bressieux, J.; Brett, D.; Britsch, M.; Britton, T.; Brook, N.H.; Brown, H.; Burducea, I.; Bursche, A.; Busetto, G.; Buytaert, J.; Cadeddu, S.; Callot, O.; Calvi, M.; Calvo Gomez, M.; Camboni, A.; Campana, P.; Campora Perez, D.; Carbone, A.; Carboni, G.; Cardinale, R.; Cardini, A.; Carranza-Mejia, H.; Carson, L.; Carvalho Akiba, K.; Casse, G.; Garcia, L.Castillo; Cattaneo, M.; Cauet, Ch.; Charles, M.; Charpentier, Ph.; Chen, P.; Chiapolini, N.; Chrzaszcz, M.; Ciba, K.; Cid Vidal, X.; Ciezarek, G.; Clarke, P.E.L.; Clemencic, M.; Cliff, H.V.; Closier, J.; Coca, C.; Coco, V.; Cogan, J.; Cogneras, E.; Collins, P.; Comerma-Montells, A.; Contu, A.; Cook, A.; Coombes, M.; Coquereau, S.; Corti, G.; Couturier, B.; Cowan, G.A.; Craik, D.C.; Cunliffe, S.; Currie, R.; D'Ambrosio, C.; David, P.; David, P.N.Y.; Davis, A.; De Bonis, I.; De Bruyn, K.; De Capua, S.; De Cian, M.; de Miranda, J.M.; De Paula, L.; De Silva, W.; De Simone, P.; Decamp, D.; Deckenhoff, M.; Del Buono, L.; Deleage, N.; Derkach, D.; Deschamps, O.; Dettori, F.; Di Canto, A.; Di Ruscio, F.; Dijkstra, H.; Dogaru, M.; Donleavy, S.; Dordei, F.; Dosil Suarez, A.; Dossett, D.; Dovbnya, A.; Dupertuis, F.; Dzhelyadin, R.; Dziurda, A.; Dzyuba, A.; Easo, S.; Egede, U.; Egorychev, V.; Eidelman, S.; van Eijk, D.; Eisenhardt, S.; Eitschberger, U.; Ekelhof, R.; Eklund, L.; El Rifai, I.; Elsasser, Ch.; Elsby, D.; Falabella, A.; Farber, C.; Fardell, G.; Farinelli, C.; Farry, S.; Fave, V.; Ferguson, D.; Fernandez Albor, V.; Ferreira Rodrigues, F.; Ferro-Luzzi, M.; Filippov, S.; Fiore, M.; Fitzpatrick, C.; Fontana, M.; Fontanelli, F.; Forty, R.; Francisco, O.; Frank, M.; Frei, C.; Frosini, M.; Furcas, S.; Furfaro, E.; Gallas Torreira, A.; Galli, D.; Gandelman, M.; Gandini, P.; Gao, Y.; Garofoli, J.; Garosi, P.; Garra Tico, J.; Garrido, L.; Gaspar, C.; Gauld, R.; Gersabeck, E.; Gersabeck, M.; Gershon, T.; Ghez, Ph.; Gibson, V.; Gligorov, V.V.; Gobel, C.; Golubkov, D.; Golutvin, A.; Gomes, A.; Gordon, H.; Grabalosa Gandara, M.; Graciani Diaz, R.; Granado Cardoso, L.A.; Grauges, E.; Graziani, G.; Grecu, A.; Greening, E.; Gregson, S.; Griffith, P.; Grunberg, O.; Gui, B.; Gushchin, E.; Guz, Yu.; Gys, T.; Hadjivasiliou, C.; Haefeli, G.; Haen, C.; Haines, S.C.; Hall, S.; Hampson, T.; Hansmann-Menzemer, S.; Harnew, N.; Harnew, S.T.; Harrison, J.; Hartmann, T.; He, J.; Heijne, V.; Hennessy, K.; Henrard, P.; Hernando Morata, J.A.; van Herwijnen, E.; Hicks, E.; Hill, D.; Hoballah, M.; Hombach, C.; Hopchev, P.; Hulsbergen, W.; Hunt, P.; Huse, T.; Hussain, N.; Hutchcroft, D.; Hynds, D.; Iakovenko, V.; Idzik, M.; Ilten, P.; Jacobsson, R.; Jaeger, A.; Jans, E.; Jaton, P.; Jawahery, A.; Jing, F.; John, M.; Johnson, D.; Jones, C.R.; Joram, C.; Jost, B.; Kaballo, M.; Kandybei, S.; Karacson, M.; Karbach, T.M.; Kenyon, I.R.; Kerzel, U.; Ketel, T.; Keune, A.; Khanji, B.; Kochebina, O.; Komarov, I.; Koopman, R.F.; Koppenburg, P.; Korolev, M.; Kozlinskiy, A.; Kravchuk, L.; Kreplin, K.; Kreps, M.; Krocker, G.; Krokovny, P.; Kruse, F.; Kucharczyk, M.; Kudryavtsev, V.; Kvaratskheliya, T.; La Thi, V.N.; Lacarrere, D.; Lafferty, G.; Lai, A.; Lambert, D.; Lambert, R.W.; Lanciotti, E.; Lanfranchi, G.; Langenbruch, C.; Latham, T.; Lazzeroni, C.; Le Gac, R.; van Leerdam, J.; Lees, J.P.; Lefevre, R.; Leflat, A.; Lefrancois, J.; Leo, S.; Leroy, O.; Lesiak, T.; Leverington, B.; Li, Y.; Li Gioi, L.; Liles, M.; Lindner, R.; Linn, C.; Liu, B.; Liu, G.; Lohn, S.; Longstaff, I.; Lopes, J.H.; Lopez Asamar, E.; Lopez-March, N.; Lu, H.; Lucchesi, D.; Luisier, J.; Luo, H.; Machefert, F.; Machikhiliyan, I.V.; Maciuc, F.; Maev, O.; Malde, S.; Manca, G.; Mancinelli, G.; Marconi, U.; Marki, R.; Marks, J.; Martellotti, G.; Martens, A.; Martin, L.; Martin Sanchez, A.; Martinelli, M.; Martinez Santos, D.; Martins Tostes, D.; Massafferri, A.; Matev, R.; Mathe, Z.; Matteuzzi, C.; Maurice, E.; Mazurov, A.; McCarthy, J.; McNab, A.; McNulty, R.; Meadows, B.; Meier, F.; Meissner, M.; Merk, M.; Milanes, D.A.; Minard, M.N.; Molina Rodriguez, J.; Monteil, S.; Moran, D.; Morawski, P.; Morello, M.J.; Mountain, R.; Mous, I.; Muheim, F.; Muller, K.; Muresan, R.; Muryn, B.; Muster, B.; Naik, P.; Nakada, T.; Nandakumar, R.; Nasteva, I.; Needham, M.; Neufeld, N.; Nguyen, A.D.; Nguyen, T.D.; Nguyen-Mau, C.; Nicol, M.; Niess, V.; Niet, R.; Nikitin, N.; Nikodem, T.; Nomerotski, A.; Novoselov, A.; Oblakowska-Mucha, A.; Obraztsov, V.; Oggero, S.; Ogilvy, S.; Okhrimenko, O.; Oldeman, R.; Orlandea, M.; Otalora Goicochea, J.M.; Owen, P.; Oyanguren, A.; Pal, B.K.; Palano, A.; Palutan, M.; Panman, J.; Papanestis, A.; Pappagallo, M.; Parkes, C.; Parkinson, C.J.; Passaleva, G.; Patel, G.D.; Patel, M.; Patrick, G.N.; Patrignani, C.; Pavel-Nicorescu, C.; Pazos Alvarez, A.; Pellegrino, A.; Penso, G.; Pepe Altarelli, M.; Perazzini, S.; Perego, D.L.; Perez Trigo, E.; Perez-Calero Yzquierdo, A.; Perret, P.; Perrin-Terrin, M.; Pessina, G.; Petridis, K.; Petrolini, A.; Phan, A.; Picatoste Olloqui, E.; Pietrzyk, B.; Pilar, T.; Pinci, D.; Playfer, S.; Plo Casasus, M.; Polci, F.; Polok, G.; Poluektov, A.; Polycarpo, E.; Popov, A.; Popov, D.; Popovici, B.; Potterat, C.; Powell, A.; Prisciandaro, J.; Pugatch, V.; Puig Navarro, A.; Punzi, G.; Qian, W.; Rademacker, J.H.; Rakotomiaramanana, B.; Rangel, M.S.; Raniuk, I.; Rauschmayr, N.; Raven, G.; Redford, S.; Reid, M.M.; dos Reis, A.C.; Ricciardi, S.; Richards, A.; Rinnert, K.; Rives Molina, V.; Roa Romero, D.A.; Robbe, P.; Rodrigues, E.; Rodriguez Perez, P.; Roiser, S.; Romanovsky, V.; Vidal, A.Romero; Rouvinet, J.; Ruf, T.; Ruffini, F.; Ruiz, H.; Valls, P.Ruiz; Sabatino, G.; Saborido Silva, J.J.; Sagidova, N.; Sail, P.; Saitta, B.; Salustino Guimaraes, V.; Salzmann, C.; Sanmartin Sedes, B.; Sannino, M.; Santacesaria, R.; Santamarina Rios, C.; Santovetti, E.; Sapunov, M.; Sarti, A.; Satriano, C.; Satta, A.; Savrie, M.; Savrina, D.; Schaack, P.; Schiller, M.; Schindler, H.; Schlupp, M.; Schmelling, M.; Schmidt, B.; Schneider, O.; Schopper, A.; Schune, M.H.; Schwemmer, R.; Sciascia, B.; Sciubba, A.; Seco, M.; Semennikov, A.; Senderowska, K.; Sepp, I.; Serra, N.; Serrano, J.; Seyfert, P.; Shapkin, M.; Shapoval, I.; Shatalov, P.; Shcheglov, Y.; Shears, T.; Shekhtman, L.; Shevchenko, O.; Shevchenko, V.; Shires, A.; Coutinho, R.Silva; Skwarnicki, T.; Smith, N.A.; Smith, E.; Smith, M.; Sokoloff, M.D.; Soler, F.J.P.; Soomro, F.; Souza, D.; Souza De Paula, B.; Spaan, B.; Sparkes, A.; Spradlin, P.; Stagni, F.; Stahl, S.; Steinkamp, O.; Stoica, S.; Stone, S.; Storaci, B.; Straticiuc, M.; Straumann, U.; Subbiah, V.K.; Sun, L.; Swientek, S.; Syropoulos, V.; Szczekowski, M.; Szczypka, P.; Szumlak, T.; T'Jampens, S.; Teklishyn, M.; Teodorescu, E.; Teubert, F.; Thomas, C.; Thomas, E.; van Tilburg, J.; Tisserand, V.; Tobin, M.; Tolk, S.; Tonelli, D.; Topp-Joergensen, S.; Torr, N.; Tournefier, E.; Tourneur, S.; Tran, M.T.; Tresch, M.; Tsaregorodtsev, A.; Tsopelas, P.; Tuning, N.; Garcia, M.Ubeda; Ukleja, A.; Urner, D.; Uwer, U.; Vagnoni, V.; Valenti, G.; Vazquez Gomez, R.; Vazquez Regueiro, P.; Vecchi, S.; Velthuis, J.J.; Veltri, M.; Veneziano, G.; Vesterinen, M.; Viaud, B.; Vieira, D.; Vilasis-Cardona, X.; Vollhardt, A.; Volyanskyy, D.; Voong, D.; Vorobyev, A.; Vorobyev, V.; Voss, C.; Voss, H.; Waldi, R.; Wallace, R.; Wandernoth, S.; Wang, J.; Ward, D.R.; Watson, N.K.; Webber, A.D.; Websdale, D.; Whitehead, M.; Wicht, J.; Wiechczynski, J.; Wiedner, D.; Wiggers, L.; Wilkinson, G.; Williams, M.P.; Williams, M.; Wilson, F.F.; Wishahi, J.; Witek, M.; Wotton, S.A.; Wright, S.; Wu, S.; Wyllie, K.; Xie, Y.; Xing, F.; Xing, Z.; Yang, Z.; Young, R.; Yuan, X.; Yushchenko, O.; Zangoli, M.; Zavertyaev, M.; Zhang, F.; Zhang, L.; Zhang, W.C.; Zhang, Y.; Zhelezov, A.; Zhokhov, A.; Zhong, L.; Zvyagin, A.

2013-01-01

The angular distribution and differential branching fraction of the decay $B^{0} \\to K^{*0} \\mu^{+}\\mu^{-}$ are studied using a data sample, collected by the LHCb experiment in $pp$ collisions at $\\sqrt{s}=7\\,{\\rm TeV}$, corresponding to an integrated luminosity of $1.0\\,{\\rm fb}^{-1}$. Several angular observables are measured in bins of the dimuon invariant mass squared, $q^{2}$. A first measurement of the zero-crossing point of the forward-backward asymmetry of the dimuon system is also presented. The zero-crossing point is measured to be $q_{0}^{2} = 4.9 \\pm 0.9 \\,{\\rm GeV}^{2}/c^{4}$, where the uncertainty is the sum of statistical and systematic uncertainties. The results are consistent with the Standard Model predictions.

Fractionation of metals in street sediment samples by using the BCR sequential extraction procedure and multivariate statistical elucidation of the data

International Nuclear Information System (INIS)

Kartal, Senol; Aydin, Zeki; Tokalioglu, Serife

2006-01-01

The concentrations of metals (Cd, Co, Cr, Cu, Fe, Mn, Ni, Pb, and Zn) in street sediment samples were determined by flame atomic absorption spectrometry (FAAS) using the modified BCR (the European Community Bureau of Reference) sequential extraction procedure. According to the BCR protocol for extracting the metals from the relevant target phases, 1.0 g of specimen of the sample was treated with 0.11 M acetic acid (exchangeable and bound to carbonates), 0.5 M hydroxylamine hydrochloride (bound to iron- and manganese-oxides), and 8.8 M hydrogen peroxide plus 1 M ammonium acetate (bound to sulphides and organics), sequentially. The residue was treated with aqua regia solution for recovery studies, although this step is not part of the BCR procedure. The mobility sequence based on the sum of the BCR sequential extraction stages was: Cd ∼ Zn (∼90%) > Pb (∼84%) > Cu (∼75%) > Mn (∼70%) > Co (∼57%) > Ni (∼43%) > Cr (∼40%) > Fe (∼17%). Enrichment factors as the criteria for examining the impact of the anthropogenic emission sources of heavy metals were calculated, and it was observed that the highest enriched elements were Cd, Pb, and Zn in the dust samples, average 190, 111, and 20, respectively. Correlation analysis (CA) and principal component analysis (PCA) were applied to the data matrix to evaluate the analytical results and to identify the possible pollution sources of metals. PCA revealed that the sampling area was mainly influenced from three pollution sources, namely; traffic, industrial, and natural sources. The results show that chemical sequential extraction is a precious operational tool. Validation of the analytical results was checked by both recovery studies and analysis of the standard reference material (NIST SRM 2711 Montana Soil)

TECHNOLOGICAL FEATURES OF MILLING AND FRACTIONATION OF FLAXSEEDS

Directory of Open Access Journals (Sweden)

A. Feskova

2015-01-01

Full Text Available Summary. The optimal parameters of milling and fractionation of flaxseeds were substantiated. It was found that the hull fraction with the highest content of lignan secoisolariciresinol diglucoside SDG was obtained when flaxseeds were grinded using a rotatory impact continuous operation mill at the rotation 1380-1640 rpm. Studies have shown that with the increasing of the rotor speed the number of unbriken seeds decreased. However, due to the fact that the shells are crushed more, they become more difficult to separate from the cotyledons. For identification and quantification of SDG the HPLC-MS method was used. It is found that the optimum separation membranes and cotyledon fraction occurs at sifting milled seeds sequentially through the sieves having meshes of 1 and 0.5 mm. The technology of industrial production of lignans-containing fraction and flour on the basis of flaxseeds processing were proposed. This technology includes milling flaxseeds at the rotation 1380-1640 rpm, with subsequent 2% silicon dioxide addition and stepwise sieving using sieves with the mesh size 2 mm. To use a fraction membranes high in lignans as raw material for biologically active additives to food it needed additional enforcement-ground to a size not more than 0.4 mm (technological features of capsulation. The developed technology allowed getting with maximum yields of lignans-containing fraction (10% yield and flaxseed flour (80% yield.

Fractional derivative and its application in mathematics and physics

International Nuclear Information System (INIS)

Namsrai, K.

2004-12-01

We propose fractional derivatives and to study those mathematical and physical consequences. It is shown that fractional derivatives possess noncommutative and nonassociative properties and within which motion of a particle, differential and integral calculuses are investigated. (author)

Sequential lineup laps and eyewitness accuracy.

Science.gov (United States)

Steblay, Nancy K; Dietrich, Hannah L; Ryan, Shannon L; Raczynski, Jeanette L; James, Kali A

2011-08-01

Police practice of double-blind sequential lineups prompts a question about the efficacy of repeated viewings (laps) of the sequential lineup. Two laboratory experiments confirmed the presence of a sequential lap effect: an increase in witness lineup picks from first to second lap, when the culprit was a stranger. The second lap produced more errors than correct identifications. In Experiment 2, lineup diagnosticity was significantly higher for sequential lineup procedures that employed a single versus double laps. Witnesses who elected to view a second lap made significantly more errors than witnesses who chose to stop after one lap or those who were required to view two laps. Witnesses with prior exposure to the culprit did not exhibit a sequential lap effect.

Optimal Exercise Boundary of American Fractional Lookback Option in a Mixed Jump-Diffusion Fractional Brownian Motion Environment

Directory of Open Access Journals (Sweden)

Zhaoqiang Yang

2017-01-01

Full Text Available A new framework for pricing the American fractional lookback option is developed in the case where the stock price follows a mixed jump-diffusion fraction Brownian motion. By using Itô formula and Wick-Itô-Skorohod integral a new market pricing model is built. The fundamental solutions of stochastic parabolic partial differential equations are estimated under the condition of Merton assumptions. The explicit integral representation of early exercise premium and the critical exercise price are also given. Numerical simulation illustrates some notable features of American fractional lookback options.

Robustness of the Sequential Lineup Advantage

Science.gov (United States)

Gronlund, Scott D.; Carlson, Curt A.; Dailey, Sarah B.; Goodsell, Charles A.

2009-01-01

A growing movement in the United States and around the world involves promoting the advantages of conducting an eyewitness lineup in a sequential manner. We conducted a large study (N = 2,529) that included 24 comparisons of sequential versus simultaneous lineups. A liberal statistical criterion revealed only 2 significant sequential lineup…

Fractional and multivariable calculus model building and optimization problems

CERN Document Server

Mathai, A M

2017-01-01

This textbook presents a rigorous approach to multivariable calculus in the context of model building and optimization problems. This comprehensive overview is based on lectures given at five SERC Schools from 2008 to 2012 and covers a broad range of topics that will enable readers to understand and create deterministic and nondeterministic models. Researchers, advanced undergraduate, and graduate students in mathematics, statistics, physics, engineering, and biological sciences will find this book to be a valuable resource for finding appropriate models to describe real-life situations. The first chapter begins with an introduction to fractional calculus moving on to discuss fractional integrals, fractional derivatives, fractional differential equations and their solutions. Multivariable calculus is covered in the second chapter and introduces the fundamentals of multivariable calculus (multivariable functions, limits and continuity, differentiability, directional derivatives and expansions of multivariable ...

Comparison of three-stage sequential extraction and toxicity characteristic leaching tests to evaluate metal mobility in mining wastes

International Nuclear Information System (INIS)

Margui, E.; Salvado, V.; Queralt, I.; Hidalgo, M.

2004-01-01

Abandoned mining sites contain residues from ore processing operations that are characterised by high concentrations of heavy metals. The form in which a metal exists strongly influences its mobility and, thus, the effects on the environment. Operational methods of speciation analysis, such as the use of sequential extraction procedures, are commonly applied. In this work, the modified three-stage sequential extraction procedure proposed by the BCR (now the Standards, Measurements and Testing Programme) was applied for the fractionation of Ni, Zn, Pb and Cd in mining wastes from old Pb-Zn mining areas located in the Val d'Aran (NE Spain) and Cartagena (SE Spain). Analyses of the extracts were performed by inductively coupled plasma atomic emission spectrometry and electrothermal atomic absorption spectrometry. The procedure was evaluated by using a certified reference material, BCR-701. The results of the partitioning study indicate that more easily mobilised forms (acid exchangeable) were predominant for Cd and Zn, particularly in the sample from Cartagena. In contrast, the largest amount of lead was associated with the iron and manganese oxide fractions. On the other hand, the applicability of lixiviation tests commonly used to evaluate the leaching of toxic species from landfill disposal (US-EPA Toxicity Characteristic Leaching Procedure and DIN 38414-S4) to mining wastes was also investigated and the obtained results compared with the information on metal mobility derivable from the application of the three-stage sequential extraction procedure

Hipergeometric solutions to some nonhomogeneous equations of fractional order

Science.gov (United States)

Olivares, Jorge; Martin, Pablo; Maass, Fernando

2017-12-01

In this paper a study is performed to the solution of the linear non homogeneous fractional order alpha differential equation equal to I 0(x), where I 0(x) is the modified Bessel function of order zero, the initial condition is f(0)=0 and 0 definition for the fractional derivatives is considered. Fractional derivatives have become important in physical and chemical phenomena as visco-elasticity and visco-plasticity, anomalous diffusion and electric circuits. In particular in this work the values of alpha=1/2, 1/4 and 3/4. are explicitly considered . In these cases Laplace transform is applied, and later the inverse Laplace transform leads to the solutions of the differential equation, which become hypergeometric functions.

Parallel Algorithm Solves Coupled Differential Equations

Science.gov (United States)

Hayashi, A.

1987-01-01

Numerical methods adapted to concurrent processing. Algorithm solves set of coupled partial differential equations by numerical integration. Adapted to run on hypercube computer, algorithm separates problem into smaller problems solved concurrently. Increase in computing speed with concurrent processing over that achievable with conventional sequential processing appreciable, especially for large problems.

Exact Solution of Space-Time Fractional Coupled EW and Coupled MEW Equations Using Modified Kudryashov Method

International Nuclear Information System (INIS)

Raslan, K. R.; Ali, Khalid K.; EL-Danaf, Talaat S.

2017-01-01

In the present paper, we established a traveling wave solution by using modified Kudryashov method for the space-time fractional nonlinear partial differential equations. The method is used to obtain the exact solutions for different types of the space-time fractional nonlinear partial differential equations such as, the space-time fractional coupled equal width wave equation (CEWE) and the space-time fractional coupled modified equal width wave equation (CMEW), which are the important soliton equations. Both equations are reduced to ordinary differential equations by the use of fractional complex transform and properties of modified Riemann–Liouville derivative. We plot the exact solutions for these equations at different time levels. (paper)

Stochastic fractional differential equations: Modeling, method and analysis

International Nuclear Information System (INIS)

Pedjeu, Jean-C.; Ladde, Gangaram S.

2012-01-01

By introducing a concept of dynamic process operating under multi-time scales in sciences and engineering, a mathematical model described by a system of multi-time scale stochastic differential equations is formulated. The classical Picard–Lindelöf successive approximations scheme is applied to the model validation problem, namely, existence and uniqueness of solution process. Naturally, this leads to the problem of finding closed form solutions of both linear and nonlinear multi-time scale stochastic differential equations of Itô–Doob type. Finally, to illustrate the scope of ideas and presented results, multi-time scale stochastic models for ecological and epidemiological processes in population dynamic are outlined.

The fractional oscillator process with two indices

International Nuclear Information System (INIS)

Lim, S C; Teo, L P

2009-01-01

We introduce a new fractional oscillator process which can be obtained as a solution of a stochastic differential equation with two fractional orders. Basic properties such as fractal dimension and short-range dependence of the process are studied by considering the asymptotic properties of its covariance function. By considering the fractional oscillator process as the velocity of a diffusion process, we derive the corresponding diffusion constant, fluctuation-dissipation relation and mean-square displacement. The fractional oscillator process can also be regarded as a one-dimensional fractional Euclidean Klein-Gordon field, which can be obtained by applying the Parisi-Wu stochastic quantization method to a nonlocal Euclidean action. The Casimir energy associated with the fractional field at positive temperature is calculated by using the zeta function regularization technique

The usage of Maxwell fractional equations for the investigation of the waveguide processes

International Nuclear Information System (INIS)

Maksyuta, M.V.; Slinchenko, Yu.A.; Grygoruk, V.I.

2016-01-01